Facebook is a social network website where people can sign up, create a profile and meet other members.  When you create an account you get your own page on the website where you can upload phots, write messages to yourself and to other members, and play online games.  When you invite someone to list on your page, you are asking them to be your "friend".  When you allow someone to be listed on your page you are "friending" them.
 
You don't have to be friends with someone (or even know them) to be "friends" on facebook.  Many poeple are friends on facebook because they belong to the same social group.