R2 means region 2; meaning this DVD will only play in DVD players that are region 2 (DVD players in Europe, Japan, South Africa, Egypt, and Middle East). For American and Canadian DVD players to play a DVD they must be region 1 (R1).
Motion picture studios want to be able to control the home release of movies in different countries because of distribution rights, copyright laws, market interest, culture differances, and the fact that world-wide releases aren't simultaneous. Therefore they required that the DVD standard include codes to prevent playback of certain discs in certain geographical regions. Each DVD 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 a disc bought in one country may not play on a player bought in another country. Some people believe that region codes are an illegal restraint of trade, but no legal cases have established this.
Regional codes are entirely optional for the maker of a disc. Players and discs are identified by their region number (listed somewhere in the technical stats of the item). Region free DVD players do exist (that play all DVDs), but are rare and expensive. A disc can have multiple regions that it can play in, or could be region-free meaning it will play in all DVD players. Before you buy a DVD from another country or online check that the region matches your player/region. So if you live in the USA and want to watch a European DVD you may want to buy a European DVD player or wait for a R1 release.
Regions and where the DVDs will play:
R0: Region Free
R1: U.S., Canada, U.S. Territories
R2: Japan, Europe, South Africa, and Middle East (including Egypt)
R3: Southeast Asia and East Asia (including Hong Kong)
R4: Australia, New Zealand, Pacific Islands, Central America, Mexico, South America, and the Caribbean
R5: Eastern Europe (Former Soviet Union), Indian subcontinent, Africa, North Korea, and Mongolia
R6: China
R7: Reserved
R8: Special international venues (airplanes, cruise ships, etc.)
R9: Undefined