A baseball glove or mitt is a large leather glove

Leather glove

A leather glove is a fitted covering for the hand with a separate sheath for each finger and the thumb. This covering is composed of the tanned hide of an animal , though it is not uncommon in recent years for the leather to be synthetic.- Common uses :A common use for leather gloves is sporting...

 that baseball

Baseball

Baseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...

 players on the defending team are allowed to wear to assist them in catching and fielding balls hit by a batter, or thrown by a teammate.
Early baseball was a game played without gloves. During the slow transition to gloves, a player who continued to play without one was called a barehanded catcher. This did not refer to the position of Catcher

Catcher

Catcher is a position for a baseball or softball player. When a batter takes his turn to hit, the catcher crouches behind home plate, in front of the umpire, and receives the ball from the pitcher. This is a catcher's primary duty, but he is also called upon to master many other skills in order to...

, but rather to the practice of catching with bare hands.