Patches come in all sorts of ways.
Here are the most common.

Protection patch = when applied to an image it will by pass the protection added to the game by the program makers.

Trainers = these add start up sequences to the game that allow you to add extra lives/shots e.t.c to the game.

Ntsc to Pal = this will give you the option of booting the game in either the Ntsc or Pal. useful if you want to play an Ntsc game on a Pal PS-2.

The most common way of adding patches to games is with Ppf-o-matic all you have to do id download the patch from megagames.com and then create a Cuesheet with CDRwin, then extract the files from the patch and with Ppf-o-matic you will then add the ppf file to the .bin file and it will tell you if it was succesfully patched.

For a more helpful tutorial there is one on my site http://www.psxcopyworld.co.uk