Helicopter rotor blades provide lift, just like airplane wings. More pitch on the blade equals a higher angle of attack, which equals more lift. The blades always rotate at roughly the same rate, so changing the angle of attack is the only way to increase or decrease lift, and therefore climb or descend. Pull the collective up and the helicopter climbs. Push it down and it descends. It sounds easy, but each move is made in concert with the other controls, so it’s not as simple as pushing or pulling a yoke.
To move the pitch of the blades, the collective is connected to a swash plate—a disc that slides and tilts on the rotor mast. Pitch change links connect the swash plate to the rotor blade. The collective changes the blades simultaneously by sliding the entire swash plate up and down.