The lid prevents air convection that carries the hot and especially wet air away. While as one answer says the resulting circulation of air cools the water, this is not the main factor. Instead, it is evaporation. Water evaporates all the time, and the closer it gets to boiling, the faster it gets.

Water uses a lot of energy to become steam, way more than it takes to get it to boiling temperatures. Every bit of steam that escapes is enough to heat way more than this amount of water all to boiling. So you want to prevent evaporation. but the speed of evaporation depends on the wetness of the air above the water. Hence a lid, to keep enough wet air inside.

And as a bonus, it prevents circulation, which would also carry away wet & hot air. Lastly, there is also a bit of energy recovered when water condenses on the lid. Condensation releases just as much energy as vaporizing takes. That effectively improves the total insulation, meaning that less heat escapes to do whatever else outside the pot.