He builds a hypothesis – candidate theory – that is somewhat naively analogous to Darwin's evolution theory in biology. Universes play the role of organisms, they may reproduce by shooting new universes from black hole singularities, and the daughter universes are somewhat different ("mutated") than their parents.
If one imagines some universal "time" in the multiverse (which is another thing that is impossible, but there are many: let's ignore all these wrong assumptions), at some moment, the population of the universes will be dominated by those in the vicinity (in the space of parameters that mutate) of universes that are most efficient in reproducing themselves. Because the reproduction rate is given by the number of black holes, this theory predicts that the parameters in our universe must be close to those for which the reproduction rate i.e. the number/density of black holes is maximized.
While the assumptions about "new universes from black holes" and all other assumptions are manifestly wrong according to our current understanding of quantum gravity – the mechanism cannot work – one may still say that the theory is falsifiable because despite the shaky foundations, it makes a prediction.
Indeed, one may look at the universe we see and ask the question whether the number of black holes could be higher. The answer is, of course, Yes, so even if you didn't care that the mechanism in the theory disagrees with some known principles of quantum gravity, the theory would still be dead because it's falsified.
It's easy to increase the number of black holes in a universe relatively to ours – in which black holes are rather rare – e.g. by choosing a smaller hierarchy (gap) between the Planck scale (of quantum gravity) and the typical energy scales of other forces.