Why does shower gel / shampoo foam a lot more on hairy than non-hairy body parts? We usually use shower gel by rubbing it on our palms and then applying it to each body part in turn in order to clean oily substances that clung to it since our last shower. This procedure does not cause the gel to foam (if it is applied to a completely hairless place, such as a clean-shaven head or back, it will produce some small amount of foam (also depending on how much you rub it); if it is applied to a place with relatively small clusters of hairs, such as arms or legs, it might foam up a bit more, and so on).

However, when applying shower gel or shampoo to a hairy place, such as the head, the groin, etc. it usually foams up significantly and rather quickly. A clear shower gel or shampoo will become a white foam in a short time.

Why is that? Is it the air trapped among the hairs?

(Please do not confuse this question with this one, they are different enough).
It's mainly due to the surface area and the spacial distribution of hair compared to that of hairless skin.  

A typical human hair width is around one micron.  Given the various hair length and thickness (space between hairs) on the different hairy regions of the body, there are orders of magnitude more surface area on which soap bubbles (foam) can adhere as compared to smooth (or even very rough), hairless skin.  

The second part of that answer, the spacial distribution, just means that the hair gives support to sustain the bubbles so they don't immediately collapse.  

Short answer, but I think this pretty much covers it.