The Outbreak was an epidemic that occurred all throughout Japan(and possibly the world).
The Outbreak was caused by an infection that turns humans into zombies. It is speculated that the infection was caused by a biological weapon. When a human is infected, they go into mindless state and their bodies turn cold and are sometimes heavily disfigured(as in the case with Megumi Sakura). These 'zombies' are drawn to humans and have an instinct to consume them. Infected humans also retain memories of their past life an example of which are the students of Megurigaoka High School.
It seems that the outbreak was predicted as Megurigaoka High School had the right facilities to facilitate humans living for extended periods of time. The school also had an underground basement in case of any outbreaks. Some teachers were also given evacuation manuals in the event the outbreak occurred.
There is also a vaccine to the infection which has "cured" Kurumi Ebisuzawa from turning into a zombie. However she still display's some zombie-like traits such as her body remaining cold and other zombies seemingly ignore her.