Picture the clubhead of an iron, made of metal. A cavity back iron is one in which the back of the clubhead has been hollowed out (creating a cavity, hence the name), as in the photo on this page. (An iron clubhead where that hollowing out is not done - where the back of the clubhead is left complete - is called a muscleback.)
Creating such a cavity in the back of an iron head removes weight from behind the center of the clubface, meaning more of the clubhead's mass is around the perimeter, or edges, of the clubhead. This adjustment to the club's physical appearance and weighting characteristics also adjusts the physics of impact between clubface and ball. And the intended result is, as noted above, an iron that is easier to hit for a wider range of golfers (larger sweet spot, higher moment of inertia, more forgiveness).
Cavity back irons can be forged, but are usually cast. Cavity back irons are preferred by mid- and high-handicap players, but also many low-handicappers and even touring pros use cavity backs, too, for their forgiving properties. Cavity back irons are far, far more common in modern golf than muscleback irons. Cavity backs fall into the category of "game improvement clubs."
For more about cavity back irons, see these FAQs:
• How do cavity back and muscleback irons compare?
• How do cast and forged irons compare?
• Do musclebacks make it easier to "work" a ball than cavity backs?