Object
Moves an object in object space coordinate system. Axis orientation includes rotations on the object itself. If several objects are selected, each object moves the same amount relative to its own object space coordinate system.
Local
Aligns the object to the rotation of the parent object. Movement is constrained to those axes in the local space coordinate system. The object is aligned to the rotation of the parent object and does not include the rotations on the object itself. If several objects are selected, each object moves the same amount relative to its own object space coordinate system.
World
Moves in the world space coordinate system. The object is aligned to the world space axis. This is the default.
Normal
Moves selected vertices or CVs in the U or V direction of the surface. Typically you would use this option for small sets of CVs. The manipulator indicates the surface Normal, U, and V directions.