If you were to put a fuel pressure gauge on the system, you'd see that when you apply vacuum to the regulator, it reduces the fuel pressure proportionately with how much vacuum is applied. At idle on a stock engine, the pressure will drop from about 39--40 down to 32 or 33 psi when vacuum is applied. As the previous poster described, the whole idea is to reduce the system pressure during low load (high vacuum) conditions when the engine doesn't need as much fuel. Keep in mind that's only one way fuel delivery is impacted. Once in closed loop, the O2 sensors work with the ecu to control air/fuel ratio by altering cycle time or pulse width (how long the injector is held open).
So, if you removed the vacuum hose or if it's getting pinched - you'd be richer during cold start up (open loop and higher fuel pressure). Once the system went into closed loop, the ecu would begin adjusting pulse width to try and reduce the amount of excess fuel that was being injected. Basically over time the adaptive strategies of the ecu would compensate for the higher pressure.
At wide open throttle, there'd be no impact from removing the vacuum line. Removing the vacuum line emulates what happens when you floor it - there's no vacuum in the intake then.