I noticed that when I do chin ups with a close grip the exercise becomes easier and I can do a lot if reps. But when I increase the distance between my hands the exercise becomes harder, so why is that?
By far the biggest different in grip variations in chin-ups and pull-ups is that between using a pronated (palms facing forward) grip and a supinated (palms facing backward) grip. Grip width often determines this, because most people find that the pronated grip feels more comfortable with a wider grip, and the supinated grip feels more comfortable with a narrower grip. (The reason for that is that both narrow grip pronated and wide grip supinated require a greater range of forearm rotation than most people could comfortable perform, with extreme pronation and extreme supination being respectively needed in order to get the hands parallel to the bar.)
The reason for this difference is that the biceps are not only responsible for flexing the elbow, they also supinate the forearm - i.e. rotate it so that the palm is facing up. Therefore, the biceps is not good at flexing the elbow when the forearms are pronated1 (i.e. palm down, or palms forward in the case of a pull-up), as the muscle would try to rotate the forearms, pulling the thumb and index finger away from the bar in the case of a pull-up. So with a pronated grip, the latissimus dorsi muscle must do more work to make up for the fact that the bicep is ineffective. This makes the exercise harder. This has been confirmed by EMG, which compares muscle activity between the different variations.2
Or, if you're talking about varying grip width while keeping the same grip type, then super-wide pull-ups are likely harder because the elbow flexor muscles are kept at an elongated length throughout the movement, which means they can't pull as hard and can't contribute as much to the exercise.