Comet Tiamat is a comet with great significance in the movie your name.. In the opening of the movie, a comet is seen falling through layers of cloud in the sky. It appears to fall onto the town of Itomori, where people are having a festival.
A comet is an icy, small Solar System body falling. When passing close to the Sun, it warms up and begins to release gases, a process called out-gassing, which gives it a stream "tail".
Itomori's primary water formation, Lake Itomori, was the result of a fragment from Comet Tiamat crashing into the town 1200 years prior to the events of the film. There is an apparently mystical connection between Itomori and Comet Tiamat, one stretching for potentially thousands of years. As stated in the film, Tiamat possesses an orbital period of 1200 years, and the comet has hit the town at least twice (once during the formation of Lake Itomori, another during the film on October 4, 2013). It is also implied, due to the size and structure of Goshintai, a large crater, that such a site was formed through another fragment of Tiamat crashing to the ground below.
The destruction of Itomori by the comet in one of the timelines in 2013 has been referred to as the "Itomori Accident".