Compression is, with EQ, one of your most powerful tool.
Basically, a compressor evens out the volume of your tracks. It turns down peaks, and turns up the quietest parts.
Use a compressor on your drums to fatten them up, and make them punchy.
Use a slow attack if you want some snap, or use a faster attack to have them fat. Another option is to send a copy of the drums to another bus, compress it heavily and blend the compressed drums with the un-compressed (or lightly compressed) original to get the best of both world.
Compress your bass track to tame the attack a little and get more sustain and body.
Use it on your main vocal tracks to turn up the quieter words that might get lost in the mix.
However, make sure to avoid over-compressing your tracks. As a rule of thumb, 3 to 6 db of gain reduction is enough. Be subtle and start with low ratio like 2:1 or 3:1.
The point is to make your tracks more consistent and punchy, so the compression should not be obvious.
You can apply compression to other dynamics instrument as well if needed (like piano for example). But for a typical rock/pop song, be sure to focus first on drums, bass and vocals.
