This is the Asphalt Roofing Manufactures Association term for a method of shingle application that minimizes roughness by keeping the number of layers of roofing closer to an even amount. It's basically butting up the tops of the new shingles to the bottoms of the old tabs. So when your roof has the older standard size shingles ( 5 inch lap ) & the new shingles are metric ( Larger 5 - 5/8 inch lap ) a re-roof costs more because the Nested method requires more roofing. Metric over metric there's no additional cost. Most roofing companies ignore the old roof & just either re-roof over it or felt it first. Even with 30lb. felting the shape of the old roof with time, heat & gravity telegraph through. Felting, for the most part, has been the only recommendation by the Manufactures to the roofers. Either way this is called bridging & leaves you with an uneven number of layers plus some other negatives: 

1. Air pockets underneath. 
2. Troughing & cupping results within 2 years & on a 6/12 or less pitch roof the water many times has run sideways under tabs ( Approx. 4 inch's ) & leaked at the side edges of the shingles below it.
3. With air pockets on application the fasteners must press the shingle all the way down to the deck & will cause a dip & many times fracture's the shingle around the fastener. Some roofers realize this & back off on the pressure which leaves the nail up. When it gets real hot these raised fasteners push up through the relaxing roofing which creates many leaks. 
4. More wind blow off potential. 
5. The roof looks thicker every 5th to 10th row consecutively on up the sections. The bottoms of these tabs are up in the air a little catching the wind & not looking uniform. 
6. Quicker aging due to the shingle rolling slightly.

All of this can be avoided with nesting, plus we feel more confident in the work & can give a longer workmanship warranty. If the roof is steeper ( less gravity & weather ) or your existing roof is the very thinnest 3 tab & your selling the home or if your roofing over thin 3 tab with a 2 ply laminate (architectural), nesting isn't as necessary. 

Nine out of ten of our owner occupied customers & five of ten rental owners chose nesting. 

We Hope this helps your decision.