Covering the pot traps heat inside the pot, mostly because you trap the steam so that it recondenses instead of escaping and the cooler air in the kitchen isn’t sucked into the pot by the lower pressure caused by hot air rising out of an uncovered pot.
Pasta water itself boils over because as the pasta is cooked, it releases starches into the water (which is why the water looks cloudy afterwards). The starches make the gas bubbles stronger and more stable, which allows them to build up rather than popping quickly. Covering the pot also means the water film of the bubbles lasts longer because vapor can recondense on it (the net loss from evaporation is slower) and so the bubbles linger.
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