Szechwan pepper is a common ingredient in Chinese and other Asian dishes. It looks like peppercorns, but is from an entirely different family of plants. It isn't hot like black pepper or chilis, and instead gives a tingle like a mild electrical current, enhancing the pleasure of other flavors.
Szechwan peppers weren't available in US until 2005 due to import restrictions, but they are becoming easier to find. Christina's in Inman Square usually has them, and many Asian markets will have them.
The szechwan peppers themselves are little round balls like normal black pepper, and like peppercorns, you grind or crush them into a power. Its best to add the powder at the end of cooking, after the dish has been removed from heat so that the chemicals that give the distinct flavor and effect are not broken down by high temperatures.
Szechwan pepper goes well with meat, fish, and vegetables that are sturdy enough to handle the flavor, and well as rice and noodle dishes. In general, if chili heat would be inappropriate for a dish, szechwan peppers are inappropriate. Szechwan peppers can be used with black pepper and chilis.
One versatile mix that you can premake in batches is a simple mix of ground black pepper, szechwan pepper, and salt, in equal amounts. This is a great rub for meats, and can be used to add extra kick to almost anything.