Categories

Hey, am very happy to use wordpress after i heard for a while so many goods on it now i know its a great platform!
Otherwise, i have an issue adding a list of cateories on the right side of my home page only. And i also dont understand what exactly is a categorie? it is a post or a page? I need a list of few genres of music i want to sell online and refered the users to the genre they want by this list.
my site is http://saiirys.com i have the LeetPress Theme.
Please Help and thank you for listening.