Flip, power move, jump with a rotation while airborne.
History
Flips entered breaking in the early-to-mid 1970s. DJ Smokey's Smoke-a-trons were known to execute flips , and presumably Grandmaster Flash's D-Squad member Flipping Mike did as well . Later, Beaver, Spy, and Trac 2 were known to do flips .
At some point, vocabulary from tricking began to influence flips in breaking.
List of Flips
There are many more flips than those listed here. Different flips may include different numbers of rotations, axis/axes of rotation, starting position, lateral movement, leg position/movement, speed, etc.
Frontflip
Also somersault. "A leap or spring in which a person turns heels over head in the air and alights on [to one's] feet" , rotating forwards (i.e. the body rotates such that the head moves towards the front).
Front Handspring
"A jump through the air on to one's hands followed by another on to one's feet" , rotating forwards.
Backflip
Like a frontflip, but rotating backwards.
Back Handspring
Like a front handspring, but rotating backwards.