Something like paper compared to metal has a different surface structure, paper is much more "bumpy" in small scale when compared, while metal is relatively smooth. The small dents and bumps are covered by electrons (obviously), and the force of these electrons against the electrons on your skin make you feel a different texture.

As for friction, which is also like texture, it's linked with the small scale bumps and dents as well. Something with high friction, like sandpaper, has a lot of these bumps and dents, which when rubbed against another material produce a force. This works basically the same as your finger not being able to go through your hand, your hand gives a force to your finger, which prevents it from going through, just in small scale.