Mainly because the lid reduces evaporation. Water evaporates all the time, not just when it's at boiling temperature. Or rather, it evaporates if the air is able to accept more water vapor. Air that is already very humid can't accept much more water. At 100% air humidity, no (net) evaporation takes place.

Okay, so why is this important to how fast water boils? Well, when water evaporates, it steals a lot of heat from its surroundings. That's how sweating cools down your body: the sweat evaporates off your skin and cools it. So, if you're trying to heat up a pot of water, evaporation is your enemy.

If you leave the pot uncovered, evaporation can happen freely as humid air above the pot is replaced by drier air. But if you cover the pot, now air gets replaced much more slowly (it will still get replaced a little). Water will evaporate into the air above it, but this air will quickly reach 100% humidity and then no longer be able to accept any more water vapor. This doesn't mean that evaporation halts completely, but rather an equilibrium is reached where some new water evaporates, but an equal amount of existing water vapor condenses against the walls and (especially) the lid of the pot. When water vapor condenses, the energy it "stole" before to evaporate is returned to the area where the condensation occurs. So, if you can get the vapor to condense inside the pot, then the heat stays inside the pot.

A smaller effect is that the lid also traps heat. Air above the water heats up, and if the pot is uncovered, this hot air is replaced by cooler air, which cools down (or slows down the heating of) the pot and the water. Trapping the hot air above the water means you again lose less heat, but the reduced evaporation will always be the larger effect.