A brayer is what a roller is called in traditional fine art printmaking. It's used for smoothing out and preparing the ink you're going to use, and for applying the ink to the printing plate you're intending to print.
Very basic brayers have plastic handles and hard rollers. Mid-range brayers have plastic handles and hard rollers held in place with metal. More expensive brayers may have wooden handles, but the significant difference is what the roller is made from. It'll be softer, with a bit more give. (Not squishy soft like a foam roller, but rubbery.) A softer roller helps get ink smooth, and into grooves.
