The idea is that by replacing some of the highly volatile fuel/air mixture with inert exhaust gas, the resulting combustion is slower and cooler, which causes more complete combustion and consequently lower harmful emissions.

The EGR Valve regulates the amount of exhaust gasses that are mixed back in.

The EGR Valve also reintroduces a larger portion of gases during the engine's first few moments running, when a necessarily rich mixture is used to get things going. The unburnt fuel in these first few moments of an engine's run can be a large percentage of its polluting output, especially if it's a modern engine in good repair. Redirecting fuel-rich exhaust gases back into the manifold does (at least) two things: one, it burns a greater percentage of the rich fuel mixture, and two, it ensures that warmer air is sent into the cold engine so as to speed up the warmup cycle.