From Bulbapedia, the community-driven Pokémon encyclopedia.
Safari Zones are special preserves for rare wild Pokémon, found in several regions. Their mechanics are not too different from each other. All have a 500 entry fee, a certain amount of time to be spent within (except the HGSS safari zone), and thirty Safari Balls, with which players may catch any Pokémon they come upon. The most important of their specific mechanics, however, is that trainers do not initiate Pokémon battles with the wild Pokémon, but instead must catch them without harming them. The wild Pokémon within Safari Zones are capable of fleeing at any given time.
Safari Zones can be found in the following regions:
Johto's National Park shares some aspects with the Safari Zones; however, these are mainly in that it is a nature preserve for Pokémon. Its thrice-weekly Bug-Catching Contest also has several likenesses to the Safari Game.
Unova's White Forest, the location exclusive to Pokémon White serves a similar function of allowing players to capture Pokémon from other regions, however there is no entry fee or limit on its use.