What is a First Day Cover?
A First Day Cover (FDC) is an envelope or card (or really anything - I have seen coconuts and rocks used to capture a first day cancellation) bearing a stamp which is cancelled on the day the stamp is initially placed on sale by the postal authorities. The specific day and location that is selected for a new stamp release is usually significant to the stamp's subject matter.
While the U.S. Postal Service designates one or more cities as "official" and provides "official" first day cancellations from those cities, today, all stamps are available nationwide on the first day of issue. This policy has created lots of opportunities for collectors to get "unofficial" first day cancellations.
Most covers have a cachet which enhances the cover by complementing the stamp and can be attractive, educational, humorous, etc. There are many different cachets for each new stamp and many different types of media are used to create cachets.
For example, this Herman Melville FDC was cancelled on the first day of issue (August 1st, 1984) in the official city (New Bedford, MA) and has a hand-drawn/hand-painted cachet by Lois Hamilton.
For more information on First Day Covers, check out the American First Day Cover Society.