They're not super rare, but you'd still be hard pressed to find one in your traditional rock'n'roll band. It's similar to a regular electric guitar in that it has six strings, but has a much larger body and heavier internal bracing to support larger strings that are tuned lower. Typically, baritone guitars are tuned a fourth or a fifth lower than regular guitars which puts it right smack dab in the middle of a guitar and a bass. The tone is nice and thick and doesn't get muddy (unless you want it to, for that I suggest a Big Muff pedal, it sounds great).
Here's a video of one in action:
https://www.facebook.com/DarlaPhilly/videos/815345301970555/
Guitarists who like to tune their guitars down to C should probably consider just getting one of these. It's more natural and just sounds better. It also sounds great when you use a slide on it for that deep country twang!