Sculpt Mode is a new mode for editing Mesh objects. Unlike Edit Mode, the model's shape is manipulated with various brushes, rather than by editing individual vertices, edges, and faces. Additionally, Sculpt Mode only edits the shape of the model (meaning vertices, edges, and polygons cannot be added or deleted in Sculpt Mode) which allows Sculpt Mode to work considerably faster than Edit Mode on denser meshes.
Sculpt Mode is primarily a tool for creating organic shapes with curved surfaces rather than mechanical shapes with flat surfaces and hard edges.
In order to customize a brush, any of Blender's textures (both procedural and image-based) can be used to control the brush shape. Texture tiling modes offer additional control: Drag simply stamps the texture on, Tile uses the texture as a tiled image across the model's surface, and 3D takes uses the 3D data in procedural textures to seamlessly apply textures across any surface.