In UnrealEd, the builder brush holds your working geometry before you subtract or add it to the map. The builder brush, when visible, is displayed as a red wire frame in all view modes. Its display can be toggled by hitting the 'b' key.
Working with the builder brush is often the easiest way to create complex architectural geometry. Rather than trying to create a detailed combination of adds and subtracts to create a intricate arched stairway, it's often much easier to use the intersect and de-intersect tools with simple base shapes to create the desired geometry entirely in the builder brush. Making geometry this way can prevent some BSP Holes (especially when used as a semi-solid). Additionally, if you merge faces before adding the geometry, it will make your map easier to texture (usually).
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