Power cycling an electronic device is a technical way of saying "resetting" it. When you power cycle a device, you turn it off and then turn it back on again. Usually, you should let the device sit for a couple seconds after turning it off to make sure the memory in the device is fully cleared before turning it back on.
Any electronic device can be power cycled, but the term is frequently used with cable modems, DSL modems, and routers. This is because small internal errors in these devices can prevent them from functioning correctly. Resetting them typically fixes the errors and allows them to work correctly again.
