Why would you use a non-contact voltage detector if you have a multimeter?
Q2: Non-contact voltage detectors don't need to physically touch the measured hardware. They work by sensing the AC electric field created by live AC wires. They're used to quickly see if there is something live, e.g. connected to a wall outlet, inside a device. You can also use them to track where power wiring is going inside a wall etc. They often also have a metal detector so you can also track wires which are not live.

Q1: "Working on a circuit" doesn't necessarily mean "debugging a circuit" here; you might not have a need to measure the circuit electrically. You might be replacing a broken plastic casing for example, and you'd use the detector to see if there's something that could give you an electric shock at the other side of the plastic before you start to fix it. 

Obviously you shouldn't rely just on the meter for your safety. You'd disconnect wall fuses or kill main switches before you start, using the meter just gives you some extra protection: with the meter you might notice for example that you've disconnected the wrong fuse and the unit is still live.