Two candidates:
1) not enough shot from the accelerator pump. When you open the throttle plate, air rushes in, and the gas can't keep up, so the engine goes way lean. So it could be lean sag. Carburetors include an accelerator pump that squirts extra raw gas into the bores when you step on the accelerator, to compensate until the fuel flow catches up. If the shot is set too low, you get lean sag.
2) having the vacuum advance on ported (or timed) vacuum, instead of manifold vacuum. Manifold vacuum sets the distributor for the current cylinder pressure at ignition in the engine to get the timing right for that cylinder pressure. Timed vacuum was introduced for emissions control, and dumps the vacuum advance at idle -- sort of "since you aren't using the engine for horsepower right now, I am going to change the tune for low emissions". When you get on it, it takes a fraction of a second for the vacuum advance to retime the distributor to what the engine actually needs to produce power.
So first move the vacuum advance to the manifold vacuum port on the carburetor, that's easy. Then, if that doesn't clear it up completely, see what your accelerator pump is set to and increase the setting.
Tell us what carb you have and we can help with more exact instructions.
