Jon Sandys

Chosen answer: It's explained in the film, although not terribly clearly. Luke's hand takes a direct blast during the fight on Jabba's sailbarge, putting a rather unsightly charred hole in it. As they leave Tatooine, Luke is seen pulling on a glove to cover the hole - he then wears it, I believe, for the remainder of the film. Presumably, with visiting Yoda and all the preparation for the assault on the Death Star, he hasn't had time to go and get it fixed.

Tailkinker ★

Answer: Additionally, from a story standpoint, when Luke cuts off Vader's hand to reveal it to be completely mechanical, he looks at his own gloved hand and is reminded what lays ahead if he turns to the Dark Side. That shot would not have worked as well if he just stared at what appears to be his normal hand, thus they found a reason to put a glove on it early on.