The snowball effect describes when somethings grows in significance or size in an increasingly faster rate. The name comes from imagining a snowball rolling down a hill - it gets larger and larger with more snow and becomes faster and more powerful as it moves onward.
It is when a situation starts small and gets built up increasing in power and momentum as it grows.
A snowball effect can be negative or positive.
An example would be a political or social situation that angered a group of people. They go to protest and they are confronted by the opposition with aggression. This would cause more attention to be focused on the situation and cause more people to become aware of it. More individuals begin to protest and the backlash increases in response. The increase in attention causes more people to become involved and causes it to build.