What is it?
An offset golf club has the club face pushed backward from the shaft. Visualize standing over a golf ball in your normal stance with the club face on the ground. An offset club will have the club face positioned further toward your back foot in relation to the shaft.
What does it do?
Because the club face is further behind the shaft, the point of impact between the golf ball and club face will change in relation to where you are in your swing. The offset will cause your club face to come around further than it would using a normal club with the same swing.
Who is it for?
Offset clubs are normally designed with the novice golfer in mind. Most new golfers slice the ball, and offset clubs give those golfers a little more time to square the club face to the ball. A cause of slicing is having the club face turned out at impact. An offset club face can help compensate for that and square the face at impact.
Offset clubs will give the ball more height than clubs with no offset. This occurs because the club face lags behind the club shaft. In doing so, the angle of the club increases as the shaft moves forward.
Some club sets are designed with static offset length, meaning the club face offset is the same for every club. Other sets have what's called a "progressive" offset style, which means the offset gradually increases with each longer club. There are also offset drivers.