A putter shaft can be straight or curved as it approaches the putter head. A shaft can be mounted in the heel or center of the putter head, as well as in between. A shaft can also be mounted into a “hosel,” a joint that extends from the putter head.
Regardless, depending on how the shaft curves and/or how the hosel is constructed, a putter can have varying degrees of “offset.”
In a putter with no offset, the leading edge of the shaft is in
direct line with the leading edge of the putter face when looking down at the putter. In a putter with offset, the leading edge of the shaft is slightly ahead of the putter face when looking down (see putter at left for example of offset, putter at right for example of no offset; graphic generously shared by Cleveland Golf).
The term “full shaft” offset means that the offset is equal to the width of the shaft, while ½-shaft offset signifies that the offset is roughly equal to half of the width of the shaft.
Offset putters are preferred by golfers who like to have their hands slightly ahead of the ball during the putting stroke. Some also believe that eye dominance plays a role in fitting offset to the golfer. In the words of Rife Putters: "For a right-handed player who has a dominant left eye, the eye closest to the hole, we would typically fit them with a straight shafted putter because that puts their dominant eye over the ball. For a person who is right eye dominant, the eye furthest from the hole, we would give them an offset shaft.
Putting the ball under the dominant eye helps the player line up the putt with more accuracy. Offset putters typically help golfers keep their hands in front of the ball at impact and promotes less break down in the wrists."
As with so many things in the world of putting, it ultimately comes down to personal preference and performance
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