The term "brush" in the Tremulous context usually refers to the brushes used by mappers (See also mapping.) to build the 3D world of a map. A brush is not something that paints color etc. somewhere (except maybe the textures that are applied to the faces of a brush). A brush is the "paint" itself. It is used to paint shapes into the 3D space.
Imagine a simple cubic room with 4 sides, floor and ceiling: All the 6 walls are brushes.
A brush does always have a volume (meaning that they are not flat or 0-dimensional) and is always convex. Convex means that it is not concave. Imagine that you bite into an apple. The resulting hole is a cavity. The apple is now concave. Before the bite, it had no cavities or indents. It was convex (please ignore the cavities at the top and bottom of the apple for the sake of this example). Rule of thumb: Concave means that you can pour coffee into it :>
Brushes can only be convex. If you see a shape that does have an opening or an indent etc., it is made of several brushes, so tight together that they seem to be one.