What iTunes Is: A music store and music library for your songs and videos, combined with a music player and cloud storage system.
What iTunes Does: iTunes is a player for all of your music, videos and streaming internet radio that allows you to manage and listen to your library of music. You can sort by artist, album, genres as well as create playlists. The iTunes Music Store allows you to buy music directly from Apple, as well as apps, audiobooks and more. iTunes can synch with an iPad, iPhone, iPod, Apple TV or your own computer. iTunes can "scan and match" your songs, which is a feature called iTunes Match. Apple uses scan and match technology to upload any songs that don't exist in Apple's iTunes library, while not having to upload any that are already there.
iCloud: You can store all of your music in iCloud, this is what allows for the automatic sync. It also includes movies, TV shows, apps, audiobooks, and games. You'll be able to listen to your music anywhere via iTunes by either 1) streaming it through an internet connection and/or 2) choosing to keep a group of songs permanently downloaded to your computer or portable device like the iPhone or iPad. On the iPhone and iPad, Apple has started calling the music player app just "Music," and using iTunes on these devices solely as a store. Podcasts are handled through an app called "Podcasts."
iTunes and the Music and Podcast apps are pre-installed on the iPhone, iPad and iPod, it's not available for Android or other mobile platforms. It is available for both Apple and Windows computer systems.