Tilt, Swing and Shift are manipulations to the optical axis of either the lens, image plane or both.
Tilt refers to the lens or back being rotated in the "up/down" direction, Swing, the "left/right" direction and shift refers to movement of in the left/right or up/down direction laterally.
Typically these movements are associated with view camera, however, there are some lenses which have a tilt and or shift mechanism built in, allowing these features to be used on an SLR format. There are also adapters which allow you to use swing/tilt with your choice of medium format lenses. Back movements on the film/sensor plane is not possible on an SLR platform.
Lens shift and back tilt/swing are used primarily for perspective control, while lens tilt and swing are used for depth of field control. It is a common misconception that tilt/shift is used only for perspective control or shallow depth of field effects. However, using camera tilt you can also manipulate the geometry of the DOF to include not only less, but more area. This technique is known as the Scheimpflug principle, for which there is a lot of technical information I don't entirely understand (and you don't need to). On a view camera using this principle with back swing or tilt, you can achieve perspective control without needing to excessively stop down to compensate for back focus.