Professional Hitter is basically a phrase used to define a player who gets hits with ease. They take advantage of bad pitches and hit them hard. They are able to handle good pitches and turn them into hits. When they get their hits it doesn't look like they were swinging wildly at the ball and just lucky, but instead looks like they had a plan the whole time.
Announcers tend to use this phrase as a way to convey to the audience that they know something about this player that the audience doesn't. Cocky bastards. Former Padres infielder Todd Walker was once referred to as a Professional Hitter despite all evidence to the contrary.