EditWhat is Lens Shift?
A projector with Lens Shift has a lens mechanism that moves up and down independent of the projector. The cost of this lens mechanism means that this feature is generally found on relatively expensive projectors.
EditWhy is Lens Shift useful?
Most projectors must be mounted in a precise position relative to the projector screen, otherwise the image projected is not centred on the screen.
EditWhat does Lens Shift do?
Lens Shift allows the position of the projected image to be moved around on the screen without needing to reposition or tilt the projector. This changes the position of the projected image without any noticeable loss of picture quality or crispness.
EditHow does this differ to keystone compensation?
Keystone compensation digitally alters the projected image to compensate for distortion of an image where the projector needs to be angled towards the screen. This is at the expense of the clarity of the projected image. Most projectors offer vertical keystone correction and some offer horizontal keystone correction. Lens Shift improves upon keystone correction by maintaining the quality, focus and overall brightness of the image.
More about keystone correction.

Simulation of difference between lens shift and keystone correction