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United States Postal Service transports letters and packages under several classifications. Each has different specifications regarding the size and content of permissible items, and the speed at which these items are sent. Prices for different services vary widely as well.
I've listed, with a brief description for each, the methods of shipment currently available from the USPS. Rates are left out because they change regularly, but if a new mail classification is implemented, this node can easily be updated. All varieties of mail listed here apply to domestic addresses; international mail is considerably more complicated and will go in another node.
First class mail: This is what people commonly think of as "mail." Weighed by the ounce, First Class mail includes letters, bills, etc., as well as small packages, which can weigh up to thirteen ounces. Rates are consistent throughout the country; you won't pay any more to send a letter to Maine than to Oregon. Delivery times are not particularly fast but usually reasonable, and United States First Class mail is generally a good value for the money, being considerably more affordable than letters sent by private carriers or by most other countries' postal systems.
Postcards: A special case of the above, postcards are sent along with ordinary First Class mail, but for a cost less than that of an ordinary one-ounce letter.
Parcel Post: Ordinary packages shipped by the Postal Service fall under this category. The USPS is a bit out of its league here, and provides rather poor competition to UPS. Parcel Post packages are weighed by the pound and sent by truck for varying rates depending on destination, similarly to UPS's standard ground service. Delivery times and costs are similar, but UPS automatically insures its shipments for no extra cost, while the USPS charges extra (exorbitant!) fees for your peace of mind. Its package-handling procedures leave much to be desired as well.
Express Mail: The Postal Service's answer to Federal Express. Packages are sent by plane to any destination in the country, 365 days a year. They're guaranteed to be there by a pre-specified time, usually the next morning. And they cost just about a fortune to send, although insurance is included in the deal for no extra charge. The USPS is so grateful for your rapid acceleration of their revenue stream that they'll even provide a free box or heavy-duty envelope for your gotta-be-there-soon stuff, at no extra charge.
Priority Mail: Like Express Mail, Priority Mail is sent rapidly by airplane anywhere in the country, and you get free packaging tossed in the deal. Unlike Express Mail, however, it's not guaranteed to be there at any particular time, and it's not insured unless you pay extra money. It usually takes two days, with "usually" being the key word here. You might think of it as a faster Parcel Post, since prices are only moderately higher than that service, while being drastically less than for Express Mail. When you factor in the availability of free Priority Mail packaging, it often results in similar costs for a significantly faster delivery time than Parcel Post.
Media Mail: This used to be called "book rate," and that's still what it's most often used for, although sound recordings and other media can now be sent under this classification as well. Books are heavy, and they're usually not particularly fragile. If you've got a bunch of books to send, can package them well, and don't mind them being treated with the lowest priority possible and rattling around in the back of postal trucks for a week or two, then Media Mail is the best way to go. It's very cheap, and big, heavy boxes can be sent all the way across the country for the same money you'd pay to have them go to the next city.
Bound Printed Matter: Occasionally cheaper than even Media Mail, but the criteria are more restrictive, and rates vary according to destination. Like Media Mail, it's used for big, clunky packages and handled by big, clunky postal employees in the back of big, clunky trucks, but these particular boxes must contain newsletters, circulars, advertising, or other literature of a similarly ephemeral quality. You might be able to sneak a few copies of War and Peace in a package, though, provided they're amply surrounded by stapled fanzines or brochures importuning the reader to Lose Weight Fast!!! I don't think anyone's looking too closely into those boxes.
Bulk Mailings: There are a wide variety of methods by which those needing to send lots of the same thing to different addresses can do so. However, these aren't generally available to the public on demand, and I've never used them or known someone who did. The commercial junk mail and political campaign flyers you receive in your mailbox have probably been sent by a bulk rate - it's easy to tell, just look at the postmark - but it's not something an individual or small business would have the occasion to use.