If you’ve just upgraded from an older iPhone to a new iPhone 5c or iPhone 5s, chances are that you transferred your data over from your old device using a backup made by iCloud or iTunes. While this is a really easy way to get your new device up and running quickly, it’s important to remember that both iTunes and iCloud store your backup based on your specific hardware device, not simply your device’s name. This means that your old backup is left lying around taking up space after you switch to a new device, while your new device creates an entirely new backup.
Once you’re sure that you’ve restored everything properly to your new device, it’s really quite easy to get rid of these old backups. For iCloud backups, go into Settings, iCloud, Storage & Backup and tap the Manage Storage option on your new device. This will show a list of all of the backups shown in your iCloud account, with the one for the current device indicated. Tap on the other backup with the same name, and choose “Delete Backup” from the subsequent screen that appears.
For iTunes, go into your Preferences and select the Devices section. This will show a list of all iOS device backups stored by iTunes. While the current device isn’t indicated here, you can probably figure it out based on the date and time shown by each backup. If you want to make absolutely sure, hovering over a backup will show additional information about the device from whence the backup came.
Simply highlight the backup you want to get rid of, click the Delete Backup button, and then click OK. Note that any backups you delete from here are not actually removed until after you click OK, so if you make a mistake, simply click Cancel instead and then return to your preferences and try again.