Time field

The Cracks in Time were, as their name suggests, 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 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 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, as seen with the Byzantium remaining crashed when the Weeping Angels, who had caused it, were erased, and Amelia Pond still existing when her parents were erased from history. (DW: Flesh and Stone, The Big Bang)

Origin
The cracks in time originated from 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 the date June 26th 2010. River Song tried to prevent the explosion, but completely lost control of the TARDIS, leaving it to explode, cracking various points in time and space, some times and places of which the Tenth and Eleventh Doctors had been involved in. This resulted in the destruction of the universe, but the TARDIS was able to preserve 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)

Earlier in the Eleventh Doctor's own 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 the former'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 was able to put his hand in it. He retrieved a piece of shrapnel from the explosion. This piece turned out to be a part of his TARDIS, which had been broken off and burned. (DW: Cold Blood)

Time Field
Some cracks released energy of pure time that could wipe individuals out of time itself and remove events from history (by removing all memory of them), 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 that 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, such as 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 her idea, and stated 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 out from the crack toward nearby people and objects.

Chronons, the elementary particles of time energy, were responsible for erasing objects from the present that no longer had a past. (VG: City of the Daleks) Whether this is related to the time energy seeping from a crack erasing individuals out of time is unclear.

Closing of the Cracks
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 was able to repair the damage caused by 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 was 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 was able to bring 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)

Notable cracks
In 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 an incredibly large size aboard the Byzantium spaceship in the 51st century. It erased Crispin, Marco, Pedro, Phillip and many Weeping Angels from existence and subsequently 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 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 vampires fled their planet because of the "silence" that they saw from 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. Just before the Doctor left, he noticed that silence fell 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, searching for "shrapnel" from the original explosion, only to find a piece of the TARDIS door, burned and destroyed. 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 erasing Rory from existence. Although the Doctor still remembered him, proven 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)
 * 1979 - A crack appeared in the portrait that someone drew of Romana. (DW: City of Death)
 * 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 so 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 - Sometime in the 51st century, a crack appeared in the secondary flight deck of the Byzantium and consumed the Weeping Angels. (DW: Flesh and Stone)

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.
 * In 2010, NASA found what appears to be a crack shaped similar to the one in Doctor Who found in the middle of the Milky Way.
 * In The Age of Steel, the Doctor said that the TARDIS had fallen through a crack in time, which is how they wound-up in Pete's World. It is unknown if this crack is related to the Time Field cracks, but it does fit as some of the cracks lead to other World/Dimensions.
 * In The Time Monster, the Doctor Mentions a "a crack in time" which might be related.
 * According to Russell T. Davies, the Doctor's closing of the Time Field also closed the Cardiff Rift..