What are the purpose of voltage doublers in flash memories?
Flash memory requires multiple high voltages for programming and erasing, on the order of 5-15V. In a low-power digital system that's probably running on 3.3V, it's convenient to have the charge pump and regulators built into the memory instead of making the external system provide 3-5 different high voltages. The high voltage supplies don't need to provide much current, and they're integrated into an IC, so a charge pump is the most reasonable converter to use.

If you want to know more about the processes that require the high voltages, look up hot-carrier injection and Fowler-Nordheim tunneling.