There are eight regions (also called "locales"). Players and discs are often identified by the region number superimposed on a world globe. If a disc plays in more than one region it will have more than one number on the globe.

1: U.S., Canada, U.S. Territories
2: Japan, Europe, South Africa, and Middle East (including     Egypt)
3: Southeast Asia and East Asia (including Hong Kong)
4: Australia, New Zealand, Pacific Islands, Central America, Mexico, South America, and the Caribbean
5: Eastern Europe (Former Soviet Union), Indian subcontinent, Africa, North Korea, and Mongolia
6: China
7: Reserved
8: Special international venues (airplanes, cruise ships, etc.)

Technically there is no such thing as a Region 0 disc or a Region 0 player.
There is such a thing as an all-region disc.

Motion picture studios want to control the home release and copyright of movies in different countries because theatre releases aren't simultaneous (a movie may come out on video in the U.S. when it's just hitting screens in Europe). Also, studios sell distribution rights to different foreign distributors and would like to guarantee an exclusive market. Therefore they required that the DVD standard include codes that can be used to prevent playback of certain discs in certain geographical regions. Each player is given a code for the region in which it's sold. The player will refuse to play discs that are not coded for its region. This means that discs bought in one country may not play on players bought in another country.

Regional codes are entirely optional for the maker of a disc. Discs without region locks will play on any player in any country. It's not an encryption system, it's just one byte of information on the disc that the player checks. Some studios originally announced that only their new releases would have regional codes, but so far almost all Hollywood releases play in only one region. Region codes are a permanent part of the disc, they won't "unlock" after a period of time. Region codes do not apply to DVD-Audio.