Twitter has launched a new feature accessible at Twitter.com that shows connections you may have with other Twitter users.
If you go to someone's Twitter profile, it will display a section in the right-hand pane (of the new Twitter design), just under the account info (tweets, following, followers, listed) that says "Connections", and displays people that are following that person and people that both you and that person mutually follow.
It's a simple and subtle feature, but one that could help build relationships on Twitter. As others have pointed out, its' similar to what Facebook does when it displays mutual friends.
The feature could actually help people use Twitter in a more social manner, as opposed to (or at least in addition to) as a news reader.
Hat tip to Carolyn Penner with Twitter Communications for pointing the feature out (as there has not been an official announcement).