The Poincaire conjecture concerns space that is connected, finite in size, and lacks any boundary. This would mean just about any type of curved 3D space. However, Henri Poincaire said, if such a space has a property that any loop in the space can be continuously tightened to a point, then it has to be sphere. The exact mathematical implications of the problem can be found HERE.
What sounds so simple is actually pretty difficult to prove. It has taken more than a hundred years for conclusive proof to be provided. The Clay Mathematics institute awarded its assured prize to Grigori Perelman. However, he refused to take it saying that his proof is based on previous works, the mathematicians of which were never recognized for their efforts. In a way, it is Perelman’s way of drawing attention to the lack of recognition of mathematician’s works unless the work is a break-through effort for any solution.
Grigori has to be applauded for standing up and drawing attention to the plight of his colleagues, even if it costs him a million dollar prize. Those who wish to know more about this million-dollar-man can check out his Wikipedia entry.