A handheld light meter will do pretty much the same as the meter in your camera - tell you how much light is reflecting off the subject, so you have a fairly good idea of how to get the exposure right. As with the in-camera meter, this works best if you meter off a grey card or equivalent. The handheld meter however may also include a cone enabling you to use it as an incident meter - which tells you how much light is actually falling on the subject, so it's fairly hard to go wrong. However the incident meter requires you to stand where the subject is and point the meter at the camera - so it's not much good if the subject is far away or difficult to reach. Finally a spot meter also tells you how much light is reflecting off the subject, but it focuses on a very precise area (or spot) so it's good if the subject is very small, or you can spot meter across the scene and work out an average.
One of the main benefits of a handheld meter is that, once you've worked out the correct exposure, the meter will tell you all the possible ways of achieving that exposure - the whole range of possible shutter speeds, apertures and ISO levels. That, and incidental metering, IMO make getting a light meter (even a cheap one) a very good idea.
If nighttime shots are what you're after, what you want to look for is the light meter with the lowest EV rating.