Poincare conjecture is a mathematical problem that is one of the millennium problems. While I don't know much about poincare conjecture, I do know a little bit about another problem that is one of the millennium problems.
P vs NP
The above link gives a good description of the problem. A short blurb I found said:
"The encryption algorithms that make virtually all electronic commerce possible work only because certain mathematical problems are very, very hard to solve. But some mathematicians are trying to prove that there's really no difference between 'hard' and 'not hard' problems--known in the math biz as P and NP."
While the poincare conjecture and P vs Np problems are entirely different, I suspect that they are fairly close to together in the hardness level. To me it is like going into space and creating a nuclear bomb. They are two different problems, which may intersect in some areas, but the main thing they have in common is that both are really hard to do. In other words, it takes a certain level of base technical advancement to be able to solve both problems. Solving one of the problems, while an achievement in itself, increases the pool of mathematical knowledge. That knowledge compounds and builds on it self and in some cases it can even implode, creating something new.
NP problems occur in many cases. Encryption is one, and if I remember my school work correctly, deciding on the shortest path is also an NP problem (think mapquest). This article describes the NP problem very well. If I understand quantum computing correctly, a quantum computer could be built which would render some if not all present encryption schemes useless.
I do not know what the solution to the poincare conjecture would affect, through it deals with mathematical shapes. Heavy duty mathematical shapes, from what i can tell, are used most in the gaming industry and by quantum physicists.