I remember the first time that I came across one of these, it was being demonstrated on "Tomorrow's World". The presenter (who was, for some reason, not the usual Raymond Baxter) touched his finger against a live mains wire and a neutral one, then leapt backwards shaking his painful, shocked, finger. But the thing did its job: he didn't die, and the electricity got switched off.
In an electric circuit, the current goes out down one wire and back along another, which is why it's called a circuit: the electricity does a round trip. With normal 240Volt mains electricity, there are three wires: the live wire for electricity going out (glossing over some details), the neutral wire for electricity coming back, and a third one, the earth wire.
The earth wire is literally connected to the Earth, so it is at the same potential as the ground, your house, and pretty much everything connected to it. The neutral wire is connected to the Earth at the power station and at various points between that and your house. There might be a small potential between the earth wire and the neutral, but not much. I have never measured more than 5 volts.
The idea behind a differential circuit breaker is that the same amount of current going out down the live wire should, in a correctly connected and functioning circuit, be coming back along the neutral wire. If it's not, then it must be coming back via the Earth, and if it's doing that, it might be getting to the Earth via your body, and this is unlikely to be doing you any good.
So the differential circuit breaker checks to see if there is a difference between the currents in the live and neutral wires, and if there is, it disconnects the electricity supply. It provides an important safety function. Its use is mandated in all new electrical installations, and all major revamps of old ones. There really is no excuse for not using them; they are life-savers and don't cost a lot.
I got one the other day to install in my fuse box that is due for a revamp. It's one for three-phase mains that I have here; the ones for normal single phase mains are smaller. You might have one already fitted in your fuse box: good. But I bet you didn't know that you're supposed to test them once a month, did you? I certainly didn't until I read the instructions that came with this one. They have a test button that if you press it should cause them to activate. The one on mine is the blue button next to the switch throw.