What does full back up of iPhone on computer means (specificly)?

See this support document which explains what is backed up with each backup method. About backups for iOS devices - Apple Support

As far as music, that is not part of the backup, as it is located in your iTunes library. You have ripped it to the iTunes library and then synced it to the phone. That would be included in your computer's backup, which would backup your entire iTunes library.

iTunes backups

From your Mac or PC, you can make a backup of your device in iTunes. Syncing your device with your computer isn't the same as making a backup. An iTunes backup includes nearly all of your device's data and settings. An iTunes backup doesn't include:

• Content from the iTunes and App Stores, or PDFs downloaded directly to iBooks (You can back up this content using Transfer Purchases in iTunes.)
• Content synced from iTunes, like imported MP3s or CDs, videos, books, and photos
• Photos already stored in the cloud, like My Photo Stream, and iCloud Photo Library
• Touch ID settings
• Apple Pay information and settings
• Activity, Health, and Keychain data (To back up this content, you'll need to use Encrypted Backup in iTunes.)

Learn how to make backups in iTunes, how to find them on your Mac or PC, and how to delete backups that you no longer need.