Transients can come from a wide variety of different astrophysical systems. Some of the most interesting things that Gaia will see are described here:
Supernovae
At the end of their lives, some stars will explode and produce a bright transient which astronomers call a supernova.
Black Hole Transients
Supermassive black holes lurking at the centres of galaxies can give rise to phenomena such as Active Galactic Nuclei and Tidal Disruption Events.
Historic Transients
Astronomy is the oldest science, and transients have been observed for longer than you might think.