Bowcasters were wildly improbable weapons designed by Wookiees. Chewbacca carried one wherever he went. It took great strength to cock the weapon, so that only Wookiees could use it. And Kyle Katarn, of course.
Essentially souped-up paintball guns, bowcasters fired heavy metal quarrels accelerated by a powerful spring, then charged the metal with some sort of vague magnetic plasma. Mounted on the tip of the barrel were two polarizing orbs on either end of a bow-shaped bar. These orbs accelerated the quarrels with magnetic fields. Fucking magnets, how do they work?!
Sometimes the guns fired quarrels, and sometimes they fired blaster bolts. Depends which game you're playing or which book you're reading. Some could fire five quarrels at a time. Some could fire magic bouncing quarrels that could somehow ricochet off walls without losing any of their momentum. They could also turn at 90 degrees in midair and trace curlicue shapes inside their victims. (Great for assassinating presidents.) Bowcasters could also fire Rambo style explosive arrows, naturally.
And they're not crossbows, OK?! They're totally different.