On several occasions, the Flash has vibrated his molecules using his superspeed powers, then passed through a seemingly solid object. What's going on here? A rather unlikely extrapolation of a concept known as quantum tunneling.
Quantum tunneling is the means by which very small particles, usually electrons, are able to pass through very thin layers of impassable materials. It depends on quantum mechanics, the way particles act at very small scales. Specifically, it depends on particle/wave duality -- at quantum scales, particles exhibit properties of both a particle and a wave. It's impossible to determine the exact position of a particle -- instead, a particle exists as a cloud of probabilities. When a particle crashes into a thin barrier, there's a tiny probability that the particle exists on the other side of the barrier. Crash enough particles and some of them will turn out to actually be on the other side when measured. Despite the name, they don't actually tunnel through the barrier. They simply appear on the other side. This isn't just theoretical -- electron tunneling microscopes measure the number of electrons tunneling through thin materials to get incredibly precise images.
How does this work for the Flash? Quantum doesn't work at macro scales. That is, entire objects can't quantum tunnel through brick walls. Presumably, Flash is vibrating his molecules to give each molecule many, many opportunities to appear on the other side of the wall. While the concept is realistic, there's actually no way a large object could quantum tunnel though anything as thick as a wall.