Hmm – it is a long time since I thought about the structure of atoms! Atoms have electrons around all the protons and neutrons. Electrons repel one another, so this must be what your friend was meaning – if the atoms that make up the molecules that make up your finger have electrons around them, and they touch a surface which will also be made of molecules, made of atoms with electrons around them. These electrons will repel each other. In practice though, the size of these things is so minute that you won’t notice any of it! That’s about as much as I can remember!
That’s probably more a question about philosophy because it depends how you define touching. All of the atoms that exist, including the atoms that make up your hand, have a nucleus in the centre and then electrons that orbit around the nucleus. Atoms are very tiny, but the electrons can actually be really really far away from the centre relative to the size of the atom, the electrons fly around the nucleus all over the place, so at any one time quite a lot of the atom is empty space.
When you touch something the electrons in your hand (or any other part of you) get close to the electrons in the atoms of the thing you are touching, electrons have a negative charge so they repel each other, this repelling force is what you feel as touching.
So if you mean do the electrons in our hands ever hit into the electrons in what we touch, or do the nuclei hit into each other then no not really, but what we define as ‘touch’ is actually electrons repelling each other, and these electrons are a part of us, so I think yes we actually do touch things!
There are four fundamental forces in nature. The strong force, which hold nuclei together, the weak force which is responsible for things like radioactive decay, the electromagnetic force that causes two oppositely charged particles to attract, and gravitation, which makes us stick to the earth and not float around.
At the atomic level, the strong and weak forces prevail, that is, they are much stronger than the other 2 forces. Their range however is very very small. On a macroscopic level, on every day life, we only experience gravitation and electromagnetic force.
So in reality, the “feel” force touching something is due to the electromagnetic force which passes on to our touch receptor on the outside of our fingers, which then get converted in an electrical signal that rushes to your brain to give you the sense of touch!