What effect does rebooting have on routers?
Often when you have issues with Internet connection your ISP might first ask you to reboot your router. If that doesn't work they will ask you to power cycle the router.
What happens when you reboot?
Routers are similar to your PC. They too have bootloader, cache memory, ROM, RAM, Processor. Yes it's more like a computer. When you reboot basically it clears the RAM. Power cycling clears the cache.
Most of the issues relating to DHCP, NAT, port connection, routing is all solved.