Other people have commented on how adhesives are made to fill in the gaps between rough surfaces. Now, the reason they actually make things stick together is that basically *everything* sticks together. It is a fundamental property of all matter that if you put it very close to each other, it sticks together (the exact reasons have to do with atoms and electrons and that opposite charges attract).
Normally when you, say, put your hand on a wall, parts of your hand will stick to parts of the wall but the effect is so tiny that you don’t even notice. The reason for that is that both the wall and the surface of your hand are still very rough at a microscopic level, so only very few points are actually touching and there is still a lot of air left in between. When adhesives fill out these empty spaces between two objects they make more atoms be closer together, and therefore amplify this fundamental “sticking force” (called the [van der Waals force](https://en.wikipedia.org/wiki/Van_der_Waals_force)) to the point where it has a macroscopic effect.
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