Addons are basically small programs that are added into your WoW game. They aren't any form of cheating or hacking, and Blizzard actually recommends some of the better ones, and sometimes even incorporates their features into the WoW game itself. They do small tasks to help you, such as remembering where you found herbs, sorting your bags, automatically equipping armor, and auto opening mail.
There are hundreds of different addons out there. My favorite site to pick them up is Curse Gaming. This site has a huge database of them, and sorts them by classes they are best for, professions that benefit from them, and categories of what they do. Be sure to read the notes on them to find out how to use them.
Not all addons are helpful. Some are just for fun and others are just plain annoying. Some don't even work, or have glitches that make gameplay very hard. Be sure to try out just a couple at a time so you don't get overwhelmed with the changes. If you don't like what an addon does, you can disable them at the character select screen. On the bottom left of the screen there is an Addons button. It will pull up a list of all your addons and allow you to check or uncheck them to disable them.
Check back with these forums to see the latest and greatest addons that people have found.