Atoms (in molecules say) keep each other at a distance to the the repulsion of their electron clouds.
For electrons to literally 'touch', they'd have to be at the same location, and the EM repulsion force (not to mention the even stronger nuclear forces) would repel at pretty much infinite force. Things can get arbitrarily close, but to touch they'd have to be at the same location, which the forces don't allow.
Hence the definition of 'touch' typically being more reasonable than that, as chiralSPO points out. Atoms are considered to be touching if their repulsion due to their electrons makes a significant contribution to the distance between the atoms.
Very interesting "infinite" force ?