Mostly a mental thing or as Bulldog19 indicates --- for show. I remember when my son was in high school he injured his wrist while catching. It was taped and within a week every catcher within 50 miles were taping their wrist. There have been times where a player has needed to reinforce the wrist and tape works quite well but ----
Baseball is a mental game and many "things" players do are based on superstition and rituals. We could start a new thread on this topic. Some players even write messages on their tape.