The Sledgehammer is a move commonly used in F2L pair insertion: R' F R F' on the right or L F' L' F' ("left sledgehammer").
|Full||R' F R F'|
|Full||L F' L' F|
Because it is a symmetry of one of the simplest non-trivial commutators (along with the sexy move), many algs and solving techniques use variations of the sledgehammer.
Use and edge control
When an edge pair that needs to be inserted rests on the left of right face of the cube relative to the face towards you, and the cross (bottom) color is facing away, usually you would have to do a cube rotation and insert it using either U' L' U L on the right or U R U' R' on the left, instead, you could utilize the Sledgehammer without a cube rotation.
This F2L pair insertion method is also often used for edge control. Instead of inserting the pair the usual way, say with U R U' R', which could leave you with a no-edges OLL, the Sledgehammer can be used to give you a more favorable, easy-to-execute OLL. This works, however, for only the final pair. If you look ahead to see that no edges are oriented for the upcoming OLL, do the Sledgehammer, and two non-existing edges will come up.
In addition to the sledgehammer itself, the inverse (sometimes humorously called Hedgeslammer) is often equally useful; it can be used if the F2L pair to insert, is facing left.
|Full||F R' F' R|
|Full||F' L F L'|
The Sledgehammer also has a popular edge-control variant that will also put up an extra two LL edges into the upcoming OLL. When the F2L pair is connected in the top layer, with the cross color facing you, doing R' F R F' on the right or L F' L' F on the left (although not as common as on the right), can also insert the pair as opposed to U R U' R'. To remember this trigger, it is the last trigger on a popular Y Permutation algorithm [F (R U' R' U') (R U R' F') (R U R' U') (R' F R F')] , and subsequently the second and last trigger on a common Key OLL algorithm [(R U R' U') (R' F R F')].