The TYPO3 Backend is the main user interface of TYPO3. Editors use it to manage pages and contents, Administrators use it to create and implement typoscript and html templates.
TYPO3 Extensions are easily installed using the Extension Manager in the TYPO3-Backend
Visitors usually fill out a form, submitting a username a password and an email address. They then get an email containing a confirmation with an activation link. After activating the user account and logging in successfully, the visitor becomes a TYPO3 FE-user.
The TYPO3-frontend is the output of TYPO3 which is usually seen by the visitors of your site.
TYPO3 is a content management system licensed under GPL with many, many features. It was "invented" in 1999 by Kasper Skarhoej in Denmark.