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 time limit (except the Johto 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 battling 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 is somewhat similar to a Safari Zone, being a nature preserve for Pokémon and having a thrice-weekly Bug-Catching Contest which shares several aspects with a Safari Game. Kalos's Friend Safari area, located in Kiloude City, also bears some similarities with Safari Zones, differing in the available Pokémon for capture (which are dependent on the Nintendo 3DS Friend Codes of other players) as well as allowing Poké Balls of any variety as opposed to solely Safari Balls.
Unova is currently the only region to have neither a Safari Zone nor anything similar to or resembling a Safari Zone.