From Quake Wiki
A brush in Quake map making is the building block of a level. Brushes are placed by the level author in a level editor and used to define the entire geometry of the level, including any solid entities such as doors, lifts and buttons.
Brushes are something that are only ever seen during the level creation process, as they are turned into a polygonal mesh during the map compilation process.
The shape of a brush is limited in that is can only ever be a convex shape. To make non-convex shapes, level authors must use multiple brushes. The reason for this limitation is that means that brushes can be defined in the .map file as a simple series of planes, the intersections of which result in the vertices of the brush that can be seen in the editor. It also makes the calculations needed during the QBSP phase of map compilation much simpler, and thus faster to run - something that was very important when Quake was being developed.