Address Book
Address book links closely with both Mail and iCal so is best considered part of the 'package'. If you enter details of all your contacts, as well as having instant searching, you can address envelopes, print labels, form groups to send e-mails to etc.
Links to Mail
When you start to type an address in Mail, it looks in your address book for the name and completes the address for you. If you create a group of friends - say Tennis Club - you can send a copy of an email to all of them by typing Tennis Club as the To address. (You can select whether all the recipients see each others addresses or not.)
Links to iCal
If you show the birthdays calendar in iCal, it collects its data from the entry in Address book - you cannot alter birthdays directly in iCal.
Synchronising with other devices
It's possible to synchronise your contacts with those on PDAs from various manufacturers e.g. Palm using either iSync (part of Mac OS X) or for more control Missing Sync from Mark Space (see links page.)