Taps are at the end of a pipe. The pipe is always full of water that is pressed out of the tap.
If the tap is closed, the water cannot come out through it. A leather or rubber disc closes the outlet that leads to the spigot.
When you turn on the tap, the wrench turns a screw that lifts the leather or rubber disc. So, water can flow out of the tap and out of the spigot. The more you open the key, further separates the leather or rubber disc from the outlet leading to the spigot and, Thus, more water comes out.
Lever taps, pedal and button
By moving a lever you can get hot or cold water. By stepping on a pedal you can make the water flow out of the tap.
By pressing a button you can get water to wash yourself. All of these are mechanisms that allow or prevent the passage of water.