Probably the most important muscle group for pull up, the biceps do the most muscle movement during. They must bring the elbow from a 180 degree angle all the way past 90 degrees while bearing the weight of the body the whole time. If you don’t have strong biceps, you won’t be able to do very many pull ups.
These muscles run along the sides of your back and are responsible for bringing our elbows. They form a lever with its fulcrum at the shoulder and often referred to as “lats”. Compared to the biceps, lats are large muscles. Therefore, they are pretty easy to build strength in. Doing a few sets of pull ups per day will strengthen them a lot.
Deltoids are located on the back of your shoulder. They help stabilize and support the shoulder joint, and they are also a supporting muscle for the latissimus dorsi and other back muscles. To build this muscle effectively, make sure you pull your chin all the way up past the bar.
From a mechanical standpoint, pull ups are a complex movement. Although the bulk of the work is done by the major muscles above, many other supporting muscles are necessary to help. They will require pretty much all the upper and some lower body muscles to some extent. This is why pull ups are one of the best whole body workouts you can do.