To say that something is "provably X" means that you can prove that it is, indeed, X. That is, if you say, "X is true", it may be a statement of opinion, or you may mean that you suspect that it is true, or you think it is probably true, but you haven't gone to any great efforts to verify it. But if you say "X is provably true", you mean that there is concrete evidence.
In this case, if someone said, "The Smith Transform is a good hash function", he might simply mean that he read the code and it looked good, or he tried it a couple of times and it appeared to work well. But if he says, "The Smith Transform is a provably good hash function", that indicates that some sort of mathematical analysis has been done, or perhaps an extensive empirical analysis, to prove that it really does give an even distribution of hash values or whatever the criteria are for a "good hash function".