Z-fighting describes an effect in the 3D design where of two or more faces of a polygon, be it a brush or mesh, occupy the same space, the very same plane actually. It creates a flickering effect where the two or more brush faces overlap. What happens is this: the engine first draws the face of one brush and then of the other, alternating between then. Should the faces have different textures the flicker effect becomes quite noticeable.
In most cases performance issues should not result, but clean overlap-free mapping is recommended.
Why is this relevant?
Eliminating these visual disruptions and technical mapping errors help the player stay immersed in the virtual world that is the map they are exploring. Since the flicking created by Z-fighting is particularly rapid and annoying it will not go unnoticed and the player will think less of the map and the level designer.