"Times Listed" refers to the number of times someone has been added to a Twitter list created by another user on Twitter. Twitter lists contain collections of users to make it easy to view only Tweets from those users.
Every time someone is added to a list, this counter goes up by one. You can find all the lists that you have been added to by going to https://twitter.com/username/memberships (replace 'username' with your account).
You can find out more about Twitter lists here https://support.twitter.com/articles/76460-using-twitter-lists