Adhesion is a phenomena closely tied to cohesion. Cohesion is the tendency for liquids to stick together like when droplets of water form. When you have something porous enough for the liquid to fall into the pores, the liquid acts as an adhesive by filling the pores and attaching itself to other molecules of its type through cohesion.
With leather, you are sweating, forming a liquid barrier between you and the leather. That sweat is filling the pores of your skin and the leather and binding you to it like an adhesive. Just like when you put a piece of paper on water on a wood table, the paper becomes stuck to the table.
If you have pores that are too small for the liquid to fill, the fluid creates a protective barrier that allows two materials to glue over the opposing sides of the fluid; this is called lubrication. Lubricants and adhesives are roughly two sides of the same coin. At least according to high school physics. I’m quite positive there are exceptions to the rules in higher level physics.
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