Vacuum assist helps by using the suction of the engine to help apply the brakes. By pumping the brakes with the engine off, any vacuum that is still in the booster is removed so that when you push the brake pedal it is only you applying the brakes.
If you then apply the brakes with the engine off you will only be able to push the pedal down so far - if you keep the pedal down and then start the engine, the vacuum from the engine then comes into play and provides the extra power to push/suck the pedal down further.
If the pedal does not go further there is likely to be a vacuum leak or a faulty booster.
Hopes this helps
Garry

