The way i understand it, the fuel combusts with a boom, creating overpressure that expands. On one side of the engine there is a big opening, on the other side - a small one.
The pressure moves the air out of the big opening, and the motion and cooling of air leaves a partial vacuum behind. Inertia of the moving air prevents it from stopping and reversing faster than the vacuum could be filled by fresh air entering from the smaller opening, which does not have a big mass of moving air in the way.
This can be achieved by two means - either a valveless that works as described above purely on the shape, or with a valve, which is held closed while the pressure is high, and then opens up as it drops, letting the fresh air into the back of the combustion chamber.
V1 is the second type, which is slightly more efficient, but somewhat less elegant and reliable (valves break, valveless have no moving parts at all).