How do virtual circuit breakers work?
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.

Related: Where are the circuit breakers on the 787?