The retopo tools make it easier to completely change the topology of a mesh while preserving the same basic shape. A typical usage of this tool is modifying a mesh to make it more suitable for animation.
Retopo works by snapping vertices in an edit-mode mesh to any 3D surface beneath the edit mesh. This is very flexible, as the base surface can be shaded bones, metaballs, NURBS, or a standard mesh. Retopo uses the depth buffer of the current view, which means that the complexity of the object being used as a base surface is does not affect the speed of the retopo tools.
With the Retopo toggle enabled (in the Mesh panel of Edit Buttons), operations that transform vertices, such as grab, scale, and rotate, will automatically snap selected vertices to any surface beneath the edit mesh. New vertices created with Ctrl+Click or extrude will also snap to other surfaces. Using this method, a new mesh can be created using the standard edit mesh tools, and the resulting mesh will automatically conform to the surfaces beneath the edit mesh.
Retopo can also be enabled for curves and surfaces in the Curve Tools1 panel. Retopo paint is not available for curves and surfaces, but all other options work the same as for meshes.
Note that you will probably want to enable xray mode in the draw panel so that your new mesh is more easily visible on top of the mesh you are retopologizing over.
In addition to the standard Edit Mode tools, topology can also be generated using Retopo Paint. This tool operates as a very simple paint brush, capable of drawing lines, ellipses, and freehand strokes. These strokes conform to the surface beneath the strokes in the same way vertices do in the regular retopo mode. Pressing Enter generates a mesh from the painted lines by creating vertices where the lines intersect and filling edges with triangles and quads where possible.
Retopo Paint Tools