From Bulbapedia, the community-driven Pokémon encyclopedia.
The Forbidden Forest (Japanese: 禁断の森 Forbidden Forest) is an anime-exclusive Grass-type Pokémon reserve. It is where May caught her Bulbasaur.
No humans are allowed in the Forbidden Forest. The folk of the nearby village try to keep travelers out. A Venusaur is the 'boss' of the Forest.
The reason no humans are allowed in the forest is that long ago, too many people came to capture the Grass Pokémon that lived there, so they became hostile toward humans and the people of the village permanently sealed off the area with a huge wooden fence.
May was kidnapped by a Skarmory and was dropped into the forest. While exploring the forest, May met a Bulbasaur trying to pick flowers. It warmed up to her and defended her against the other Grass Pokémon, who saw her as a threat. When May left the forest, Bulbasaur decided to go with her.
Pokémon seen in the Forbidden Forest