Why do insects ant most animals lay many eggs at a time?

They are r-selected species, which means their reproductive strategy is to produce as many tiny offspring as possible and invest as little energy and care into them as they can. Because they are so tiny and have no parental care, almost all of them die before becoming adults, but that doesn't matter because there are so many of them. Their populations exist far below the carrying capacity of the environment, so they have adapted to be able to fill the environment with as many offspring as possible without worrying about running out of resources.

This is as opposed to a K-selected species like a human or bear, where only a few relatively large offspring are produced, and lots of energy and parental care are invested in them. These species exist in populations near the carrying capacity of the environment and therefore they cannot produce hundreds of offspring at a time without draining all the environment's resources and causing a population crash.