Time field

The Time Field was a field of time energy that spilled from mysterious cracks in the fabric of time and space caused by the TARDIS exploding on 26th June 2010, after coming under the control of an unknown entity, whose voice was only heard repeating the line: "Silence will fall."

Cracks
The cracks were described by the Eleventh Doctor as "two parts of space and time that should never have touched". They were present in the very fabric of spacetime - a crack that appeared to be part of a wall would still be there if the wall were removed. (DW: The Eleventh Hour)

According to Rosanna Calvierri, the cracks ranged in size from tiny to "big as the sky", and some connected to other worlds, while others led only to "silence, and the end of all things". (DW: The Vampires of Venice)

Some cracks acted like wormholes, and could be opened to allow a passage between the places on either side. One device known to be able to open such a crack was a sonic screwdriver. (DW: The Eleventh Hour) Rosanna Calvierri and her family traveled through such a crack to Earth (DW: The Vampires of Venice), as did Prisoner Zero. (DW: The Eleventh Hour)

Regardless of the size and what was on the other side, all cracks appeared to be of the same shape and orientation. When they erased people and events, the consequences would still remain; the Byzantium remained crashed when the Weeping Angels, who had caused it, were erased, and Amelia Pond still existed when her parents were erased from history. (DW: Flesh and Stone, The Big Bang) Some cracks released energy of pure time able to wipe individuals from time itself and remove events from history, though time-travellers such as the Doctor still had the ability to remember them, at least so long as the removed event or person did not relate to the person's direct past. (DW: Flesh and Stone, Cold Blood) The Doctor guessed such cracks had erased events such as the CyberKing walking over London in the Victorian era and the Dalek invasion of 2009, one of Earth's most publicly visible invasions, explaining why Amy Pond did not know about those events. Smaller, inconsequential things were erased as well, including, perhaps, the ducks from a duck pond in Leadworth.

The Doctor stated that the only way to close such a crack was for it to consume a complicated space-time event, such as himself or a large group of Weeping Angels (all of them together being equivalent to himself). River Song volunteered to let herself be consumed, but the Doctor laughed at the idea, and said that she wasn't even as complicated as one Angel. (DW: Flesh and Stone)

This time field was visible as a glow of bright white light, which sometimes extended tendrils from the crack toward nearby people and objects.

Origin
In the Eleventh Doctor's personal timeline, when sealing the crack in the hull of the Byzantium, he traced the origin of the crack to a temporal explosion on 26th June, 2010. (DW: Flesh and Stone) This day was to be the wedding of Rory and Amy, but after Rory's death and removal from existence by a crack, the wedding plans no longer existed.

When a crack appeared in 2020, underneath a small village in Wales, the Doctor put his hand in it. He retrieved a piece of shrapnel from the explosion. This turned out to be a part of his TARDIS, which had been broken off and scorched. (DW: Cold Blood)

The cracks in time originated in the destruction of the TARDIS when it came under the control of an unknown, disembodied, external force, which forced it to materialise outside of Amy Pond's house on June 26th 2010. River Song tried to prevent the explosion, but completely lost control of the TARDIS. It exploded, cracking points in time and space, some of which the Eleventh Doctor had been to. This resulted in the destruction of the universe, but the TARDIS preserved Earth by putting itself in a time loop at the moment of its death. The heat from the perpetual explosion heated the alternate Earth in place of the sun. (DW: The Pandorica Opens, The Big Bang)

Closing
Having determined that the Pandorica - designed as the perfect prison - still contained some atoms of the original universe that existed prior to the TARDIS exploding, the Doctor flew it into the heart of the TARDIS explosion. Using the remaining atoms of the real universe inside the box and the restoration field, he repaired the damage from the cracks. The universe and the time line were reset as a result, with all of the cracks closing, never existing, and the versions of Amy and Rory relevant to the old time line, erased. However, in order to fully close the cracks, the Doctor had to allow himself to be absorbed by one and be erased from existence. Using the ability given to her by the crack in her room, Amy's remembrance of her parents and Rory undid their erasure in the rebooted universe. The Doctor, however, remained erased until Amy remembered him and their adventures and brought him and the TARDIS back. Despite everything being repaired, the Doctor still remained clueless as to what was responsible for the destruction of the TARDIS in the first place. (DW: The Big Bang)

It is implied in Series 6 that the religious order, The Silence, were behind the attempted destruction of the TARDIS and the cracks in time, but their exact motives for doing so have not been made clear. It is possible that this was an early attempt to kill the Doctor to prevent him from reaching Trenzalore, since The Silence may not have expected him to allow River to fly the TARDIS without him, nor anticipated the resulting cracks in time.

Notable cracks
Around Easter of 1996, a crack in Amy Pond's bedroom connected to an Atraxi prison. This crack also took away Amy's parents. (DW: The Eleventh Hour, The Big Bang) Cracks also appeared on the side of Starship UK in the 33rd century (DW: The Beast Below) and in the Cabinet War Room in 1941. (DW: Victory of the Daleks)

Another crack later opened to a vast size aboard the Byzantium spaceship in the 51st century. It erased Crispin, Marco, Pedro, Phillip and many Weeping Angels from existence and then closed. The Weeping Angels had feared it, and attempted to escape, only to be dropped into it after they absorbed all of the Byzantium's energy, disabling the ship's artificial gravity. The Angels, combined, were a sufficiently complex space-time event to seal it for a while. (DW: Flesh and Stone) The crack was mentioned again in Venice, 1580, when Rosanna Calvierri claimed that she and the other Saturnyans fled their planet because of the "silence" they saw through some of the cracks. They passed through one of the cracks that led to "an ocean like ours", which turned out to be the Earth, after which the crack closed behind them. After the Doctor saved Venice, one of the cracks appeared in the sky, slightly moving. Just before the Doctor left, he noticed that silence had fallen over Venice. (DW: The Vampires of Venice)

There was a crack beneath the Earth in 2020 that the Doctor, Amy and Rory found while leaving the Silurian base. Attempting to investigate the crack, the Doctor reached inside for "shrapnel" from the original explosion, only to find a burnt piece of the TARDIS. Before leaving, Rory was shot by the Restac, and came in contact with the light from the crack before the Doctor and Amy could rescue him. Despite Amy's efforts, the Doctor was forced to leave Rory behind. The crack erased Rory from existence. Although the Doctor still remembered him, as demonstrated by the Doctor mentioning him in later episodes (DW: Vincent and the Doctor) and the engagement ring which he bought Amy still existing in the TARDIS, Amy lost all recollection of Rory due to the crack directly affecting her past. (DW: Cold Blood)

There was a crack in Craig Owens' flat in 2010 in the kitchen, next to the fridge. The mysterious Time Field energy began to emit from it, and the crack began to expand. (DW:The Lodger)

Another crack appeared in the TARDIS whilst it was parked next to Amy's house on 26th June 2010. The TARDIS monitor read "LOCATION: Earth, DATE: 26/6/2010", until the glass cracked into the shape of the cracks. This was followed by a sinister voice rasping "Silence will fall". (DW: The Pandorica Opens)

Chronological appearances

 * 1929 - A crack appeared on one of the walls in the temple of Artemis. (NSA: The Hounds of Artemis)
 * 1941 - A crack appeared on the wall of Winston Churchill's Cabinet War Room. (DW: Victory of the Daleks)
 * 1996 - A crack appeared on young Amy Pond's bedroom wall, connecting it to an Atraxi prison. This was when the Doctor first noticed them. (DW: The Eleventh Hour) The crack was still active when time was reset and was forever closing. The Doctor, deciding to skip the rest of his rewind and knowing he had to be on the other side of the cracks for them to close completely, stepped into the crack, erasing himself from history until Amy remembered him. (DW: The Big Bang)
 * 2010 - A crack appeared on a screen in the TARDIS before the Doctor turned it off. (DW: The Eleventh Hour)
 * 2010 - A crack appeared by the side of the fridge at the house of Craig Owens. (DW: The Lodger)
 * 2010 - A crack appeared on a screen in the TARDIS, followed by an unknown voice repeatedly saying "Silence will fall" soon after River Song left the TARDIS. (DW: The Pandorica Opens)
 * 2010 - A crack appeared on the TARDIS screen. (DW: The Big Bang)
 * 2010 - A crack appeared on Aickman Road as the Doctor's time line rewound. (DW: The Big Bang)
 * 2020 - A crack appeared in the rock of a Silurian base. After Rory Williams was shot, it consumed him and he was erased from time. The consequence of this was that Amy Pond forgot about him, with only the Doctor remembering him. (DW: Cold Blood)
 * 3295 - A crack appeared on the side of the Starship UK. (DW: The Beast Below)
 * 41st century - Some time in the 41st century, a crack appeared on a tank that held a Dalek creature. (GN: The Only Good Dalek)
 * 51st century - Some time in the 51st century, a crack appeared in the secondary flight deck of the Byzantium and consumed the Weeping Angels. (DW: Flesh and Stone)

Trivia

 * When the Trickster fooled Sarah Jane into saving her parents, it caused a crack in time at the Abbot's Gateway. If this is a similar wormhole crack that Rosanna used is unknown.

Behind the scenes

 * The time crack was inspired by a crack Steven Moffat saw in his son's bedroom, which resembled a smiling mouth.
 * In the Doctor Who Confidential episode for The Big Bang, Steven Moffat revealed that the Silence (and presumably the voice heard in the TARDIS during The Pandorica Opens) will be explained more in Series 6. (CON: Out of Time)
 * The cracks provide a retro-continity explanation for how the world in Doctor Who can continue to be similar to our own despite multiple public alien invasions, extra wars, historical interences, mass disapearances, inconsistant technological breakthroughs, and unexplained astrological phenomena. Whenever such an event occurs, it is erased or at least smoothed over by the cracks.
 * In 2010, NASA found what appears to be a crack shaped similar to the one in Doctor Who in the middle of the Milky Way.
 * According to Russell T. Davies, the Doctor's closing of the Time Field also closed the Cardiff Rift.