He has a glove on his left hand that i filled with vaseline to keep his hand soft for when he is with his wife.
Thats all it says in the book about it.
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Candy mentioned that Curley wore a glove filled with Vaseline on his left hand to keep it soft for his wife. Curley's wife enjoys soft things, so he wears the glove to maintain a soft touch for her.
Curly was trying to beat up Lennie after Lennie had laughed at him, so Lennie got very scared and grabbed on to Curleys hand very hard and he crushed it so hard that it broke and it bled.