Strobes are essentially large flash units. They use a flash tube for a "bulb." The advantage is a much more intense (stronger) light that is color balanced to film. You also don't have the heat that hot lights (bulbs) create so the room doesn't heat up (especially in Texas summers!) and nobody gets burned by touching a light accidentally. They're less of a fire hazard, use less electricity overall, they last a lot longer than photo flood bulbs, and provide a much more even lighting on the subject. Since digital does allow for white balance, it's not as huge an issue as it is with film. With film you need to use what are expensive bulbs rated at the right temperature to balance with daylight film, or buy special tungsten balanced film. Alien Bee's, and most better strobe systems, also allow for adjusting the intensity of flash, much as you do with the dedicated flash unit you use on the hotshoe of your camera. With a strobe system, you plug directly to your camera to trigger the lights, or can trigger them with a camera mounted flash (most strobe systems have slaves built in).
This photo was shot in my friend's living room using 3 Alien Bee strobes. One in a softbox, one bounced with umbrella, and one as a hairlight directional to the background, which was seemless paper (this final image has had the background knocked out and replaced). Note the lack of shadows, especially around the eyes, glasses, and nose. This can be more difficult to achieve with hotlights and requires more frequent adjustments on the direction or barndoors.
