The snowball effect refers to a system where increasing momentum makes it easier to keep increasing momentum. The name comes from pushing a snowball down a hill; the bigger the snowball, the more snow it picks up as it rolls and becomes still bigger. Eventually you don't have to push the snowball because it rolls under its own weight.
In gaming, snowballing usually involves a finite system where resources are used to acquire the means to obtain more resources. The more you have the more you can get, and the more you get the less is available for anyone else. So the player who takes the initial lead is much more likely to be able to keep it and increase it.