The gloves in this excellent short story only actually occur once, and are used to trigger off another one of Walter Mitty's famous daydreams, but also are used to reveal more of the character of Walter Mitty and the kind of weak, spineless man he actually is. Consider how these gloves are first introduced:
"Why don't you wear your gloves? Have you lost your gloves?" Walter Mitty reached in a pocket and brought out the gloves. He put them on, but after she had turned and gone into the building and he had driven on to a red light, he took them off again. "Pick it up, brother!" snapped a cop as the light changed, and Mitty hastily pulled on his gloves and lurched ahead.
The way in which he has to be reminded about the gloves by his wife almost suggests that he is a child being told to dress warmly by his mother, and this is an impression that is supported by the childish way in which he takes them off when she leaves. When he is challenged by another authority figure, he puts them on again, as if to cement his own weakness and the way that he is not a strong character and allows others to dominate him. The gloves also allow him to daydream about being a famous heart surgeon in the next daydream.