This may be hard to explain but let's see if I can...

While it is certainly good advice to hit standard putts in the sweet spot of the putter face, occasionally you'll face a downhill breaker that you could easily hammer through the break...hitting the ball offcenter (we're talking hair's breadth, not "less than 1 inch or so") will deaden the blow and "shave" it right or left depending of which side of center you use. Say you have a right-to-left downhill putt that needs to start precisely on the lip but will roll straight and miss if you hit it too hard...the technique is to aim ever-so-slightly (a dimple or two) inside the lip and strike the ball off-center toward the toe...that deadens the blow and sends the ball that dimple or two to the right of where you are aimed, producing the desired result. Works the same way on left-to-righters, only you strike it off-center toward the heel.

Having said all this, I wouldn't advise average to poor putters to employ this technique...imo this is for better, more experienced putters only...even then it's only worth attempting in certain slippery situations.

Shade