The Beast's Forest, as its namesake implies, consists mostly of trees that form a large, dense forest. There's also a mountain range running right next to it.
The Wild, Wild Pussycats have an office located somewhere in the forest. Within the office, there are cabins where visitors can stay, featuring a dining hall, hot springs and dormitories.
During the Forest Training Camp Arc, the Beast's Forest was used as a boot camp for the students of Class 1-A and Class 1-B in order to improve the strength and effectiveness of their Quirks. The students first had to fight through Pixie-Bob's Earth Flow monsters within the forest before arriving in the Pussycat's office, which served as their lodge for the trip. Pixie-Bob would later use her Quirk once again to build a training area for the students next to the office.
Later, the League of Villains' Vanguard Action Squad attempted a surprise strike on the Beast's Forest, taking advantage of the environment to attack the students. One part of the forest was lit on fire by Dabi, with another part being covered by Mustard's poisonous gas. Fumikage Tokoyami's Dark Shadow also left considerable damage to the forest. The wildfire ended up being suppressed by the firemen shortly after the League retreated.