I leave mine physically switched on all the time.
Rebooting the router means restarting it from scratch (ie pull the power lead out and plug it back in, flick the switch off/on etc) Resync means to renegotiate your connection with the exchange. This occassionally happens to me - the SNR margin gets so low the connection to the exchange drops and the router automagically reconnects.
Ian Stirling
Sky Broadband Max