(covers information from several alternate timelines)
A hand was an anatomical appendage that had developed on many humanoid species, the primary function of which was grasping, holding, typing, etc. The hand played an integral part in the sense of touch, since many humanoid species used their hands for tactile feedback.
Humanoid hands tended to vary with both number of hands and number of digits on each hand: Voth and a species from Tau Alpha C had three fingers per hand, while Humans had five; as well, Edosians had three hands, while Terellians, and a pianist on Qualor II, named Amarie, had four hands.
Vulcans seem to place more significance on their hands than humans, possibly because they use their hands to mind-meld, which is taken very seriously in Vulcan society. Vulcans press their fingers together as a gesture of affection, akin to a kiss (First seen in Journey to Babel).
In 2151, Doctor Phlox treated Crewman Alex, who had first-degree burns on his right hand, from the seal of a nitrogen valve having blown when he had been trying to reroute the valve. The hand injury (and a similar burn on Alex's forehead) was treated with dermaline gel. (ENT: "Dear Doctor")
In 2267, the being who claimed to be the Greek god Apollo captured the USS Enterprise by generating a powerful force field in the shape of a giant green hand. This encounter was one of several witnessed by the tardigrade "Ephraim" during her attempts to be reunited with her eggs. A legend of a similar giant green hand was told in the alternate reality as one of the possible causes of the disappearance of the USS Franklin. (TOS: "Who Mourns for Adonais?", ST: "Ephraim and Dot", Star Trek Beyond)