Time field

A Time Field was a mysterious crack in the fabric of time and space caused by an unidentified explosion that originates from 26/06/2010.

Origin
The cracks in the universe were said to come about from an explosion. After sealing the crack in the hull of the Byzantium, the Doctor traced the origin of the crack to a temporal explosion on the 26th June, 2010. (DW: Flesh and Stone) This day was to be the wedding of Rory and Amy, but at the former's death and removal from existence by a crack, the wedding plans no longer existed.

When one appeared in 2020, underneath a small village in Wales, the Doctor was able to put his hand in it a 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)

Varieties of crack
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 released energy of "pure time" that could wipe individuals out of time itself and remove events from history, though time-travelers 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) Such cracks seemingly 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.

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)

Other 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)

Regardless of the size, and what was on the other side, all cracks appeared to be of the same shape and orientation.

Notable cracks
In Easter of 1996, a crack in Amy Pond's bedroom connected to an Atraxi prison. (DW: The Eleventh Hour) A crack 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 were forced to flee their planet, which was being consumed by a crack. She also claimed that they saw two different types of cracks; one through which they saw other worlds and people and the other through which they saw only silence and the end of all things. According to her, the cracks could be tiny, or as big as the sky. Just before the Doctor left, however, silence fell over Venice, which he picked up on. (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 Silurian, 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 it is implied that the Doctor may still remember him, and the engagement ring which he bought Amy is still visible in the TARDIS, Amy has lost all recollection of Rory due to the crack directly affecting her past. (DW: Cold Blood)

Chronological appearances

 * 1580 - Rosanna Calvierri and her people, having seen the cracks, and fearing the ones that led only to silence, fled through one that led to Earth, which then snapped shut behind them. (DW: The Vampires of Venice)
 * 1941 - A crack appeared on the wall of Winston Churchill's Cabinet War Room when the TARDIS left.(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 appearing. (DW: The Eleventh Hour)
 * 2020 - A crack appeared in the rock of a Silurian base. After Rory Williams was shot, it consumed him, so that Amy Pond forgot about him, and only the Doctor remembered him. (DW: Cold Blood)
 * 3295 - A crack appeared on the side of the Starship UK, just after the Doctor had left. (DW: The Beast Below)
 * 51st century - Sometime in the 51st century, a crack appeared in the forest inside the Byzantium and consumed the Weeping Angels. (DW: Flesh and Stone)

Behind the scenes

 * The Time Crack was inspired by a crack Steven Moffatt saw in his son's bedroom, which resembled a smiling mouth.
 * Moffat has confirmed that the Crack will appear in most episodes.
 * The Cracks arc is, like the previous series (excluding the Bad Wolf meme), foreshadowed in a previous series, in this case in DW: The Next Doctor (though, perhaps unintentionally).
 * The Time Field has caused much debate amongst fans, with many "supposed Cracks" that are actually just clouds and other items of scenery (e.g., small cracks in the walls under the Earth in Cold Blood and clouds and lighting giving the impression of a crack in the sky in The Vampires of Venice).