Here's a simple way to think of it. Compression makes loud sounds quieter and quiet sounds louder so that everything ends up sounding the same volume. Now this is a very simple way to put it, but it is a place to start.
aaronmcoleman gave a great description, but to make it a little simpler:
Ratio: How much compression is applied, the higher the ratio, the more likely everything has the same volume (Loud gets quiet, quiet gets louder)
Attack: How fast the compressor reacts to loud or quiet and brings them to an equivelent level.
Release: When the compressor lets go and lets the signal return to it's uncompressed level.
Knee: You can set the compressor to appy more compression the louder (stonger) the signal gets. On a graph, it makes a curve and where it bends is called the knee. Sharp bend you get strong compression at that point, gentle bend, the compression is less aggressive.
Gain: Like mentioned, raises the entire volume.
Best to play with it and get a feel for what it does. Also, a lot of compressors sound different and can color the sound in a pleasing (or horrible) way. Take the time to experiment. Compression can make a track great, and poorly used, can ruin it as well.
Good luck and welcome!