I tried to google the answer, but I could find nothing about it: how does a virtual breaker physically work? I know how you control it, but what really happens when you press the breaker switch button on the MFD?
Virtual breakers use solid-state relays:
A solid-state relay (SSR) is an electronic switching device that switches on or off when a small external voltage is applied across its control terminals.
The relay may be designed to switch either AC or DC to the load. It serves the same function as an electromechanical relay, but has no moving parts.
According to Boeing for its 787:
The remote power distribution units (RPDUs) are largely based on solid-state power controllers (SSPC) instead of the traditional thermal circuit breakers and relays.
The standards for the solid state power controllers in aircraft is set by BS ISO 8816.
A virtual circuit-breaker is a relay (solid-state or otherwise) where the current going through it is monitored by a computer of some sort. When the computer sees too much current going through it, the computer trips the relay open. (Think of it as 'active CB' versus 'passive CB'.)
The engineer/pilot can access the computer to find out which CBs have been tripped by the system, and can try to get the system to close them again, just like resetting a real CB.
Advantage 1 - you can guarantee that the CB will trip at the target amperage, a real CB will often have a large error in its trip amperage.
Advantage 2 - real CBs have to be mounted where they're accessible to the crew, virtual CBs can be mounted anywhere that's convenient for the systems design engineer.