Flash meters are a lot less common in the bags of photographers since the transition to digital cameras. The main reason for that is that most photographers, amateurs or pros rely on their cameras for a correct evaluation of light and exposure. This is fine, up until one point. Today's DSLRs and mirrorless cameras do a terrific job at reading ambient and natural light. They really make buying a separate light meter almost useless. So if you're a 100% natural light photographer, read no further.
But if you use flash or studio lights often, buying a flash meter could make your life a lot easier. Things get a little more complicated when you add one or more different light sources in the scheme and that's probably why many photographers chose to work with natural light only. However it's only hard until you get the hang of it. There are two ways to set your flashes correctly and get the results you're looking for.
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Number is one is good old fashioned trial and error. You get the model, the camera, and the flashes and start experimenting different lighting setups and exposure values. It's the best way to learn and it's also very effective at achieving different looking results. But it's slow, especially if you're not someone who's been doing it for years. That can lead to the model losing patience, to frustration and so on.
The other way is to use a flash meter. There are many different ones out there, ranging from basic models that only show you the correct aperture setting to much more advanced models that have built-in radio triggers and a lot of other cool features.
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A flash meter is a lot easier to use than you would be tempted to think. It works by giving you a solution based on the exposure values you dial into it. You're still going to have to practice the first few times, but after you learn how to use the flash meter, you won't want to start shooting without it
Here is a great video tutorial on how to use flash meters from AdoramaTV.