The "S" in EF-S has variously been described by Canon as coming from either "Small image circle"[1] (the lens projects a smaller image circle than normal EF lenses to match the sensor), or "Short back focus"[2] (the smaller mirror used in APS-C cameras also allows optical elements to protrude further into the camera body, reducing the minimum distance between the sensor and the back element of the lens).
Although not all Canon EF-S lenses use this short back focal length, they cannot be mounted on DSLRs with sensors larger than APS-C.
However, some lenses produced by third-party manufacturers may feature the standard EF mount if they do not have the shorter back focal length but only have a small image circle.
Some have reported success attaching EF-S lenses to full-frame bodies with the use of an extension tube; however, this does not eliminate the vignetting problem, and also removes the lens's ability to achieve infinity focus.
This modification comes with caveats, one being that on some lenses, like the EF-S 10-22mm, at the 10mm setting, the element protrudes too far back toward EF mount camera bodies.