Chapter 2.1 BSP Brushes: Overview

Utilizing BSP Brushes / CSG
BSP Brushes are the most basic of the building blocks in Unreal. Conceptually, it is best to think of BSP as carving out and filling in volumes of space in your level. BSP was once used as the primary building block in level design, but now more efficient and differently specialized geometry types have been introduced. However, BSP can still be useful in the early stages of a product, for rapid prototyping of levels and objects. This doc goes over what BSP can be used for as well as explaining how to use it.

Technically, BSP (Binary Space Partitioning) refers to a data structure that is used to organize objects within a space, and thus it is not semantically correct. A more accurate term for this type of geometry would be CSG (Constructive Solid Geometry). Both terms BSP and CSG are used interchangeably in Unreal.

Previously, an empty level was a solid space - in effect an additive space. Now, the level starts out as a subtracted space. What this means is that you no longer need to start out with an initial subtraction when creating your level.
http://udn.epicgames.com/Three/UsingBspBrushes.html

Brush Properties
Existing brushes can be edited by selecting the brush and right-clicking in the viewport to access the context menu. Note that the right-click menu is always accessible, and is context-sensitive, showing different options depending on what you currently have selected in the editor.
http://udn.epicgames.com/Three/UsingBspBrushes.html#BpAnchor

Geometry mode
Geometry mode gives the level designer much greater control over their BSP geometry than was ever possible with vertex editing. Vertex editing is still supported, of course, but you can now also manipulate entire polygons and the edges between them as separate entities.

The best part is that you can do all of this without worrying about the integrity of your BSP data. The editor will keep track of what you're doing and will handle most situations automatically. Collapsing a polygon will see it silently removed from the brush, moving a vertex off of a polygons plane will see that polygon automatically triangulated to compensate, etc. Geometry Mode gives you a lot of power but also offers a safety net.
http://udn.epicgames.com/Three/GettingStartedWithGeometryMode.html