"Power Cycling" means to briefly remove power from the eGauge in order to cause a hard reboot. No stored data is lost when performing a power cycle. Power cycling is most often done in situations where the eGauge webserver interface is not responding, or ub other issues like if network changes invalidate the DHCP lease, power cycling the eGauge will cause it to request a fresh lease and become available faster.
In most installations, the eGauge (not to be confused with the HomePlug adapter) is powered directly from a circuit breaker or breakers. In your breaker-panel, locate the breaker to which the eGauge is wired. This breaker should be labelled "eGauge Disconnect" or something similar. In a residential installation, it is usually a two pole breaker (similar to that used by a stove or dryer). In buildings with three phase power (typically large commercial/industrial settings), it will be a three pole breaker. Some services outside the United States may only use a single pole breaker (single phase power).
The EG4xxx model eGauge can be rebooted from the LCD screen by navigating to Tools -> Reboot. This will usually result in the same outcome as actually power cycling the eGauge.
Once you locate the breaker, trip it so power is off, wait 5 seconds, then turn it back on. Normally, there is a single multi-pole breaker for eGauge, but in some cases there may be two or three separate breakers (one per phase/leg). In the latter case, turn off all eGauge breakers, leave them off for 5 seconds, then turn them all back on.