The Cosmological Argument is an argument to try to prove that God exists. The idea is that since everything in the world has a cause, there must have been a first cause, or a cause of everything else. This first cause was God.
In other words, to understand the Cosmological Argument, it helps to think of a chain of events. Every event at the end of the chain has a cause, and we can trace this chain back and back until we get to the start. This start is what the Cosmological Argument is trying to prove was God.