iTunes in the Cloud puts your purchase history in the cloud so that it downloads your iTunes purchases across all of your devices.
iTunes Sync? I presume this is Wi-Fi Sync. Self-explanatory there.
iCloud Backup is exactly what it says it is: backup to iCloud. It does not require iTunes. In fact, it replaces iTunes as the backup device. Your backup files are uploaded into the cloud servers at Apple's data centers instead of local backups on your hard drive.