A presta valve is different from the schrader valve which is found on a car. When you pump a schrader valve, the pump has to mash down the little pin in the middle of the valve for air to get into the car tire or bicycle tube. See this picture:
The presta valve is different. Instead of a spring which closes the valve, it simply relies on the higher pressure inside the tube to push the valve closed against the lower air pressure outside the tube. When the little nut on the top is screwed down, that is just like extra insurance to keep the valve closed because the pressure inside the tube should already be pushing the valve up keeping it closed. To pump air through the presta valve into the tube, you push on your pump which increases the outside pressure (in the pump hose of a floor pump or in the barrel of a minipump itself) to a higher pressure than what's inside the tube, and that pushes the presta valve open. Typically the pressure in the tube and in the pump hose will then be equalized. When you disconnect your pump, then you're releasing the pressure on the outside of the presta valve and the high pressure in the tube pushes the valve shut.
So what does all this mean? First, you have to have the little nut at the top of the presta valve loosened so the valve can open and close. When the nut is tight, the valve is closed tight so air cannot pass through the valve. Secondly, you don't need to mash down the pin in the middle of the presta valve during pumping because the pump pressure is enough to push air through the valve. People recommened quickly "burping" the valve before attaching the pump head simply because the valve can be a little "sticky", so "burping" it quickly makes sure it moves freely when you try to pump it. Thirdly, it's important that your pump head seals decently to the outer part of the valve stem because you need enough of a seal for the pump to increase the pressure going through the pump hose higher than the pressure already inside the tube. If the pump head leaks at a lower pressure than the pressure you want to pump the tube up to, the air from the pump will leak out from between the pump head and the valve stem instead of going through the presta valve into the tube.