What is a Multi-wire Branch Circuit?
A multi-wire branch circuit is two or more circuits that are served by a set of hot wires connected to different phases (all with the same voltage between them) and a common neutral wire (all of the hots also have the same voltage with respect to the neutral). This arrangement saves a bit on wire and can also save on conduit fill. The NEC in paragraph 210.4 (b) requires a means to disconnect all of the hot wires simultaneously. Typically this would be a single multi-pole circuit breaker.
The simultaneous disconnect requirement serves to protect against the possibility that someone working on the circuit wouldn't notice that it was a multi-wire branch circuit and would disconnect the neutral while another wire in the circuit was energized.
That said, you may run into multi-wire branch circuits that are protected by individual breakers, especially in older construction or in panels that have been modified without attention to the code (or thinking through the consequences of working on the circuit with one of the hot wires still energized).
In most residential applications multi-wire branch circuits would be 3-wire (two hots and a neutral) with 240 Volts phase-to-phase and 120 Volts phase-to-ground, but you might run into 4-wire circuits in buildings with 3-phase service (for example a high rise urban apartment building).
How do I know I have one?
You have to look carefully. There are several clues in the panel:
If the breakers in the panel are labeled you may get a clue by noticing that a multi-pole breaker is serving non-appliance circuits (e.g., something other than a 240 Volt appliance like a stove, oven, hot water heater, or dryer). Don't count on the labels being right…
Next look for any multi-pole breakers rated at 15 or 20 Amps. Most, *but by no means all, 240 Volt appliances will have 30 Amp or higher breakers. If any of those breakers serve a 120 Volt circuit – for example lighting or outlets – you've almost certainly got a multi-wire branch circuit. The exceptions that I can think of are outlets integrated with appliances, like a 120 Volt outlet on a stove.
Finally look for a single pole breaker with a colored (not black) wire on it. Follow that wire back to where it comes into the panel. If it is part of a cable (as opposed to a set of wires run in conduit) follow the other wire (presumably the black one) and see if it runs to a breaker (it might be unterminated as a spare). If it does, you've got a multi-wire branch circuit. It would be a good idea to replace the single-pole breakers with a multi-pole breaker and bring all of the wires in the circuit to it.
What do I need to do differently when working with one?
The big thing to know is that you've got two circuits that are interconnected because they share a neutral wire. If they are on single pole breakers and you don't notice you could get a shock working with a neutral that you thought was dead.
Another potential problem is that you can't use a single-pole GFCI on a multi-wire branch circuit.
Finally you need to ensure that the hot wires on single-pole breakers are out of phase with each other. Typically this is ensured by putting them on adjacent breakers in the panel or better yet, put them on a multi-pole breaker.