Easiest way to describe a full-frame sensor is to say when you mount a 35 mm lens on it the resulting image is one shot at 35 mm, not 45 or 50 as would be the case with most digital camera today. IOW, the 35-mm equivalent of any lens is the same as the lens.

Plenty of links on this -- for example

Generally full-frame sensors are on pretty high end cameras, but Canon has one for around $2500 as I recall. Of course, some would say $2500 is high end.