What does it mean for two objects to "touch"?

If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of "I'm not actually touching you! The electrons in the atoms of my skin are just getting really close to yours!" Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects. Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other. So what does it mean for two objects to touch each other? Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either? Is there really no such thing as "touching"?