I know that exercises like pull ups and chin ups incorporate your back muscle but I don’t understand how. Your arms are doing the whole movement of lifting you up.
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If you’re performing them with just your arms then you’re doing them incorrectly.
From a totally hanging position you must tighten your lats and pull your scapulas together and downwards before engaging your arms.
Whenever you’re wondering about muscles used, look at the joints that are moving and the muscles which attach to those joints.
In order to pull yourself up, you have to rotate your elbows and your shoulders.
Closing the elbow is done by a bicep muscle.
Movement in the shoulder is achieved using the [latissimus dorsi muscle](https://www.yoganatomy.com/wp-content/uploads/2015/03/latissiums-dorsi-fi.jpg) (the popular “lats”). As you see in the picture, the muscle is attached to the spine and to the arm, and its function is to pull the arm closer to the body by rotating the shoulder joint. That’s what happens when you’re doing the pull up.
[Here’s a neat animation](https://media.giphy.com/media/JizXYNONuHjX6oIg8e/giphy.gif) of what lats (back muscles) do in a pull up.
Downward rotation of scapulothoracic joint (scapula movement against rib cage), adduction of glenohumeral joint (shoulder) both use muscles on your back. You can google these separately to find more detailed answers about which exact muscles will be activated.
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