Explain how a population of insects could become resistant to a pesticide?

Ironically, from being exposed to the pesticide for a long period of time. Given a long enough timeframe, a insect species will evolve a natural resistance to a chemical through natural selection.
Insects quickly develop resistance to insecticides due to natural evolution. As their bodies are exposed to the chemicals, small changes are made until it no longer affects them over many generations.
some insects will have an adaptation that helps them survive and that they pass onto their offspring.
the insect population changes to include more and more resistant members

Answer:
This is evelution in action.
If the insects are exposed to a pesticide that only kills some of them, the only future generations come from resistant parents. If the application if pesticide continues, it weeds out non resistant individuals enhancing the resistence of subsequent generations.