People occasionally ask me about handheld light meters. Let me preface this by saying, I do not use a separate light meter and I find them to be a waste of time and money for digital photography. Having said that, some photographers really like them, even for digital.
The handheld light meter is a bit of tech from the days of film when you could not immediately see the result and histogram of your image on the back of the camera, or in the computer if you are shooting tethered. A good light meter will be able to measure a few different things, ambient light, incidental light and reflected light, as well as telling you these measurements for a single light source or the combination of multiple light sources including strobes. Before digital this was very important for being able to get an accurate idea of what the separate lights were doing. In the days of film this was very important since it might be a couple of weeks before you would see the effort of your labors - to much time and expense later to have to correct a lighting mistake. Handheld meters did something the primitive built in camera meters of the day could not do.
When using a hand held meter you take several readings as you are setting up, one for each light source at least. The short version if you are using strobes as your primary light source is to set the meter to your ISO and aperture settings on the camera and the meter will tell you the power to set your strobes. (Shutter speed in this case being used to control the amount of exposer from ambient light sources.) However the handheld meters will only be accurate to within about 1/2 a stop. A few things will prevent it from giving you the exact exposure you need. The clarity and type of lens you are shooting with for example will effect how the light falls on the camera sensor, this is just one of many things a handheld meter will not measure for.
How is this different from what you would do if you set up without a handheld meter? Its not really. The old built in meters on cameras like my mother's Fuji Rangefinder were very primitive and basically could tell you - there is this much ambient light coming from this direction. The meters built in to cameras now can get very specific spot and even point readings of that light now, which will tell you how many stops of light you need to add or subtract from the image as it would expose with ambient light on a specific point in the frame. This lets you be very specific with what you want to expose for in the frame, somebodies cheek for instance. You can then also check to see how the window next to them will expose just by shifting the point you are measuring (most cameras measure the same point they use to focus.) As you are setting up and turning on your lights you can take test shots and compare the image and histogram to what you expect based on your meter readings and light settings and adjust as needed, basically combining the metering for the lights with your test shots and saving a little bit of time in set up, eliminating the need to then adjust for errors. And more importantly saving you the expense of a separate tool and the batteries to run it.
The most important thing in photography is what light is getting to the sensor or film. The built in camera meters have come a long way in the kind of readings they give you. This combined with the instant image on the screen and the histogram telling you the complete dynamic range of the image I personally have found handheld meters to be an unnecessary step. In most cases I can have the lights set for the exposure I want in two to three test shots. This is something a handheld meter wont tell you, it will give you a reading based on an 18% grey world and guess on how you intend for the light to interact with your photo, meaning that after you take the time to meter, you will still probably need 2 or 3 test shots to fine tune your lighting.