This meaning refers to the large padded glove worn by baseball players, especially catchers and fielders.
He caught the ball in his mitt.
The player bought a new leather mitt.
This broader meaning refers to a mitten or protective glove with the fingers partly or fully enclosed together.
Use an oven mitt to remove the tray.
She wore thick mitts in the snow.
This informal meaning refers humorously or critically to a person's hand.
Keep your mitts off my phone.
He held the sandwich in one enormous mitt.