What does it mean when a man plays with his wedding ring when talking to a woman he gets on well with?

it means he likes her and would give up his marriage for her

ANSWER:

I think this married man is trying to hide his ring by covering his finger away from her so she wouldn't see that his married, and that's my only opinion. If you noticed the only married men who don't hide their wedding band and having affairs are the one who works with a woman in the same company. For others they will removed their ring as soon as they're out of their house. With my husband, he took it off so the women he meets on a dating site will know that he is not married.