Hasta simply means the hand, and almost everything about this star follows from that. An open hand gives. A working hand shapes. A closed fist grasps, or holds on to something it should have released.
In Hindu mythology, Savitar is the solar deity who impels: the one who sets things in motion at the start of the day. If you have ever recited the Gayatri Mantra, you have already addressed him. The line Tat Savitur Varenyam names Savitar directly, which makes the most widely recited mantra in Hinduism the mantra of this nakshatra's deity.
That gives Hasta an unusual character. Savitar supplies the impulse, the hand supplies the execution, and between them the star is about turning an intention into a finished thing you can hold.
Its shakti (the special power a nakshatra carries) is placing the object of desire into your own hands. Not receiving it. Getting it yourself, by skill.
Hasta is known for dexterity and craft. Natives tend to be good with their hands in some literal way: cooking, surgery, drawing, repairing, playing an instrument, or the kind of practical fixing that makes a household run. The connection with palmistry comes from the same symbol, and many traditional readers of hands are said to carry this star.