Content such as music, videos, apps, etc. never get restored from backup. It would be useless since they should already by in your computer in your iTunes library.
Syncing and backing up the phone only saves other stuff, such as app game/file saves, text messages, settings, etc. Stuff that is not content.
When you restore from backup, it restores all the settings and that's it. Then you need to sync the phone as you normally would to put back all the music, apps, videos, etc that is sitting in your iTunes library. Usually this happens automatically when after it is restored. Sometimes it doesn't and you need to manually click the sync button.
If you don't have your apps in your iTunes library, you'll need to re-download them all. Stuff you previously paid for should be downloadable for free.