Don't look for "the" structure. He is referring to the fact that the crystal structure of a protein doesn't actually represent the only structure that the protein can adopt.
The figure shown here illustrates one of the problems with referring to the structure of a protein. This is a representation of an NMR structure of bovine ribonuclease A. It shows that various parts of the protein exist in several different conformations. The actual protein structure is a composite of all these structures in equilibrium with each other.
These conformation could be considered "breathing" and you may think they're not important. However, there are many cases where the conformations of a protein are quite different. We are familiar with allostery, where the conformation of a protein changes when it's bound to a ligand, but the are also examples where two very different structures exist in equilibrium in the absence of ligand.
Read his blog posting and keep in mind that proteins are dynamic structures and not static rigid crystals.