Twitter Login connects your site's users with Twitter by...
This means that new visitors to your C5 can now elect to signup using Twitter if they wish with one click.
Twitter Login maintains a lookup table cross-referencing Twitter credentials with C5 users and once authenticated via Twitter, Twitter Login also stores the user's credentials in the current session, allowing other blocks and PHP code to take advantage of being able to perform Twitter actions for the user.
Please bear in mind that no representations are made to the security of the Twitter association and the C5 user account though all C5 user actions are performed through the C5 library and all Twitter actions are performed via the OAuth interface so the account associations should be as secure as your own site/server setup.
When a user is asked by Twitter to allow the App access to their Twitter account, the App name presented by Twitter to the user is 'Log - In'. This has changed from 'Concrete5 Login' by request.