It's an approach for finding a counterexample, in case that smoothness fails. The idea is to find scaling-down blowups for Navier-Stokes type problems, so that a solution near his kind at scale A reproduces a very similar solution at scale A/2, and so on to A/4 until you get a singularity at a finite time. He has given a rather beautiful and nifty way of doing this construction in systems which are very similar formally to Navier Stokes, but modified so that he is able to control the reproduction process at each stage, and prove stability, so that little changes don't wreck his constructions.
The main thing about his method is that it requires that the fluid is actually capable of storing information stably for long enough to construct the next smaller stage, and this is likely false in the highly chaotic world of the turbulent systems, but who knows, it needs to be investigated thoroughly. Unlike other problems, Riemann Hypothesis, or Yang-Mills mass gap, this Clay problem we don't know the answer for sure, there might be a surprise.
If the solutions to Navier Stokes are actually smooth, which is more likely given present knowledge (although not certain), then his method will not solve the problem, rather they will work to exclude certain avenues of proof.