Super glue is made from a small molecule called ethyl cyanoacrylate.
When these small molecules contact water, even the only very slightly dampness of dry fingers or wood, they quickly join up into long chains (polymers) that bond surfaces (such as fingers) together.
Superglue forms a strong bond with wood, plastic, and leather. It is used to lock nuts onto bolts because while it bonds well to metal, it has a low shear strength, so the nut can later be removed from the bolt using a wrench.
Formulations of super glue have been made for medical use, to glue wounds together without stitches, and to slow bleeding.
Cyanoacrylates react strongly with cotton, generating heat and smoke, and can in some cases cause the cotton to ignite. They also react strongly with baking soda (sodium bicarbonate). This is sometimes useful, and filling a hole with baking soda and then adding super glue can make a strong space filling material.