The Great Breakout was a period in history, around the year 5080, in which humanity spread out to the stars. This also meant the solar system became busier as large numbers of frontiersmen and pioneers became concentrated in the asteroid belt while waiting to spread out in the Galaxy.
The Fourth Doctor noted that the spread of humanity at this time was like a tidal wave or a disease. He added that when humans got together in large numbers, other lifeforms sometimes suffered. (TV: The Invisible Enemy)
This event apparently took place several hundred years after the Revolution of the Ood, at which time the Second Great and Bountiful Human Empire already controlled three galaxies. (TV: Planet of the Ood) Notably, around the same time, World War VI broke out between regional superpower blocs on Earth, although it was resolved swiftly by the collapse of the heavy-handed Supreme Alliance. (TV: The Talons of Weng-Chiang)