I'm gonna go pretty basic and say:
Addons help game play, make things easier :)
http://wow.curse.com/downloads/addons/
This website is the safest to download from.
Ones that I find useful are:
Titan Panel (This gives quick functions, and shows extra information, like how much gold you have, if you need to repair, how long you've been playing, etc.)
QuestHelper (super popular- this basicly tells you where to kill and where to go for quests.)
Auctioneer (Gives you prices from the auction house)
Cartographer (super popular- this gives you co-ordinates on the map, they're suprisingly useful)
DamageMeters-
SWStats- These last two are good for tracking dps and heals while in a group or even on your own.
Others include:
Omen- A Raiding mod, Im guessing you probably wont need this yet.
Deadly Boss Mod- Another raiding mod, this is useful in battlegrounds too.
Group Calender - this is a guild calender, it's good for scheduling events
Good Luck, and if you need any other help, feel free to email me, which you can access via my Yahoo Answers page. :)
EDIT:
he he, I just thought of something. You might not know how to add them! lol
Ok, so you download them.
Then you usually "unzip" them, To do this, right click on the file, and press "extract files here" or something similar. Then you will need to move those files in to the game files.
Now here's the part to listen to:
1. You need to put them into your Game file. So you need to find out what Hard Disk it's on. If you don't know already, you can
"Right Click" on the desktop icon or icon in your Start Menu,
and press "Properties",
Look at the box that says "Target", and it will say a drive, for example mine says D:\Program Files\World of Warcraft
You will have something similar.
2. Go to the location by opening a new 'Windows Explorer' or 'My Computer' screen, and going folder by folder to the World of Warcraft one.
3. Double click on the WoW folder
4. Double click on the Interface folder
5. Double click on the Addons folder
6. Copy the files that you extracted from the download, and paste them into this folder.
7. Launch WoW, and you can alter which addons are used etc. from the character screen after you login.
Good Luck, and if you need any help, or have questions, feel free to email me, which you can access via my Yahoo Answers page. ^_^