Crossover pipes quiet the ex. noise, and increase bottom end power. It does the latter by helping to kill the return pulse in the pipe, thereby keeping the ex. flow velocity up, which means better combustion chamber evacuation/less intake charge delution.
Another way to describe it is, it's a "collected" system, something like 4-into-1 headers, or tunnel ram intake manifolds. It's all about dampening system pulses (which tend to restrict flow, whether ex. or int.).