A finger turn is a classical ballet term describing a step where the girl is turning while being partnered by a male dancer. Their only connection during the turn is, as you can guess, by the fingers or hands.
A finger turn is typically done with the male dancer slight behind and to the left of the ballerina with his right arm raised over, but out of the way without crowding the space, her head. He extends his middle finger straight downwards as the others are straightened up to be parallel with the floor. The ballerina then holds on, lightly, to the male dancer’s middle finger by cupping her hand, as if she was holding a marker in her hand. There is usually one preperation for these kinds of turns, which is where the male and female will have their left arm extended to the side. The male will keep his arm strong and in a proper position for the ballerina to then push off, gracefully, and fold her arm into first position while keeping the grip loosely on the male dancer’s finger as she pirouettes around.
Finger turns are very often seen in classical pas de deuxes, as well as a lot of contemporary ballet.