Unplugging a router from the wall socket
What you are waiting can be two things.  One is for the ISP to "release" your dynamic IP address, and after 'x' minutes, when powered back on, the MRC (Modem/router combo) will be re-assigned an IP address to its MAC address. 

The other reason is to allow a internal capacitor to discharge completely to allow the volatile memory that contains the cache to be cleared. Clearing this cache can often "resolve" the issue.