The Millennium problems are not necessarily problems whose solution will lead to curing cancer. These are problems in mathematics and were chosen for their importance in mathematics rather for their potential in applications.
There are plenty of important open problems in mathematics, and the Clay Institute had to narrow it down to seven. Whatever the reasons may be, it is clear such a short list is incomplete and does not claim to be a comprehensive list of the most important problems to solve. However, each of the problems solved is extremely central, important, interesting, and hard. Some of these problems have direct consequences, for instance the Riemann hypothesis. There are many (many many) theorems in number theory that go like "if the Riemann hypothesis is true, then blah blah", so knowing it is true will immediately validate the consequences in these theorems as true. A solution to some of the other problems is (highly likely) not going to lead to anything dramatic. For instance, the $P$ vs. $NP$ problem. I doubt anybody in the world thinks it is even remotely slightly conceivable that $P=NP$. The reason it's and important question is not because we don't (philosophically) already know the answer, but rather that we don't have a bloody clue how to prove it. It means that there are fundamental issues in computability (which is a hell of an important subject these days) that we just don't understand. Solving $P \ne NP$ will be important not for the result but for the techniques that will be used. (Of course, in the unlikely event that $P=NP$, enormous consequences will follow. But that is about as likely as it is that the Hitchhiker's Guide to the Galaxy is based on true events.)
The Poincare conjecture is an extremely basic problem about three dimensional space. I think three dimensional space is very important, so if we can't answer a very fundamental question about it, then we don't understand it well. I'm not an expert on Perelman's solution, nor the field to which it belongs, so I can't tell what consequences his techniques have for better understanding three dimensional space, but I'm sure there are.