Much like the name suggests, Address Book is a program that stores contact information such as email addresses, phone numbers, mailing addresses, etc.  The program's real functionality is in its ability to integrate with other OSX programs.  Most common is to store email addresses (or groups of email addresses) for use in composing email.  However the contacts in your Address Book can be used in iCal to send reminders about events, in iChat for buddy lists, to autofill forms through Safari, to send faxes, and a whole lot more.