A multi-wire branch circuit is two circuits sharing a single neutral - two hots from different legs of a 240V panel, each with their own breaker, sharing one neutral conductor. The idea is that the neutral only carries the unbalanced current between the two legs, so under balanced load conditions, the neutral carries close to zero. It’s a legitimate code-allowed wiring method (210.4) that saves you a wire.
The rules: the two breakers MUST be on opposite legs - that’s what makes the math work. If they’re on the same leg, the neutral carries the sum of both circuits instead of the difference, which can overload the neutral. This is why 210.4(B) requires a “simultaneous disconnect” - a two-pole breaker or a handle tie. Without it, someone can kill one breaker and think the circuit is dead while the neutral is still energized from the other circuit. This is a shock hazard.
The AFCI issue: modern AFCI breakers do not like MWBCs because the shared neutral confuses the arc detection. In practice, many electricians avoid MWBCs in new work and just run separate circuits - the wire savings don’t outweigh the complexity with modern protection requirements.