What are contacts? Someone made me a contact, now what?
Adding someone as a contact is a simple way to keep track of their contributions on the site. You can have up to 750 contacts. To add a contact, go to that person's profile page and click on the "Add user as a contact" link there. You can choose what your relationship is with this user, or leave that part blank.*
Making someone a contact allows you to easily see some of their site actions in your Contact Activity sidebar on the front page: you can see if they make a new post, make a comment that gets more than 12 favorites, get a "best answer" in AskMe, or add contacts. You can also see their activity on the My Contacts page. If you have made someone a mutual contact -- you have linked them and they have linked you -- you will be able to tag each other's posts in AskMe and MeFi.
The most common reason to add someone as a contact is that you enjoyed a comment or post they made, and you want to see future things they post. There is no obligation to be reciprocal if someone has added you as a contact.
When you add a user as a contact, this information will be visible on your own user page as well as your usercontacts page. Contacts you have added are listed in your profile with the phrase "Links to", and people who have added you as a contact are listed under "Linked by".