A Total Event Collapse was a time explosion, which caused the universe to totally collapse, hence the name "Total Event Collapse."
A total event collapse can be caused by a TARDIS exploding, as shown when the Doctor's TARDIS exploded. The Doctor seemed to have knowledge of them and knew that the only way to stop a total event collapse was to try and reboot the Universe. Some things could survive a total event collapse if they were at the centre of the explosion, before they were also erased from existence, as happened with the Earth.
The Doctor noted that every sun would "supernova, at every moment in history" and that "the whole universe will never have existed", meaning the total event collapse caused every star to supernova, at every point in history. While Earth's sun went supernova, Earth itself survived as it was at the "eye of the storm" (with the explosion itself acting like the sun and warming and heating the Earth) and it and Earth's Moon survived up until 1996 when the collapse started to cause Earth to erase as well.
The Doctor was able to stop the total event collapse by using the Pandorica, which contained some atoms of the former universe, and flying it straight into the heart of the TARDIS, causing the Big Bang Two which reset the universe.
Time travel was still possible after a total event collapse, but only at the heart of the explosion. A total event collapse also seems to change some species' histories. A Cyber Leader noted that "all universes will be deleted", which suggests a total even collapse also affects parallel worlds.