Adding pasta to boiling water slows the contents down to a simmer, cooling the water from a boiling temperature of 212 degrees Fahrenheit to 185 to 205 degrees Fahrenheit.
If you don't bring the water back to a boil, you'll be cooking the pasta at a slower temperature, resulting in a mushy texture. It also risks having your noodles clump together.
The second boil is also a great time to add salt. Boiling water will dissolve the salt more quickly and prevent the salt from falling to the bottom, where it can scratch the pot.