"+5 V Standby" is provided by a separate voltage regulator, which continues to work even when the PC, including the rest of the ATX PSU, is shut down.
"+5 V Standby" typically can provide up to 2 A, i.e. up to 10 watt, though some old PSUs may be able to deliver only up to 5 watt and some of the bigger ATX PSUs may be able to deliver up to 15 watt.
Besides supplying the Ethernet cards, to enable WoL, "+5 V Standby" can be used by the USB ports if configured so in BIOS, to enable waking the PC with the keyboard, or to enable charging from USB even when the PC is shut down.