The backup contains:
- All your settings
- Application data except data marked as "cache" or not to sync.
Since iOS 5 there is a possibility for the developers to exclude some items from the backup.
There are ways to explore your backup, but I don't think this could give you definitive answer, wether your backup is complete or not. Developers should make sure that they don't exclude items from backup that cannot be recreated in some ways (download, rebuilding & etc). Some movie players offer to disable backups for their content, but this is configurable.
Because TED content can be downloaded at any time, probably the developers decided to not backup video content. Check the app for settings.
iTunes stores the most recent backup of your iPhone in ~/Library/Application Support/MobileSync/Backup/[ID] iTunes does not keep any history of your iPhone backups. It is a copy of the current state of your photos and other data on the iPhone.
To recover an earlier version of your iPhone backup relies on however you backup your Mac.
Time Machine backups include the MobileSync folders. So you could retrieve an old iPhone backup from Time Machine, replacing the current backup in ~/Library/Application Support/MobileSync/Backup/[ID], and then restore your iPhone. This would, of course, replace all your current photos (and other data) with that from the old backup. Probably, not quite what you want.
I suggest using iBackupBot which is able to open any folder on your Mac containing iPhone backups. So find an old iPhone backup in Time Machine, retrieve the whole folder to your Desktop (or somewhere convenient) and open it with iBackupBot. Your photos will be in the Media/DCIM/100Apple/ folder. You can then extract these to your Mac.
If you don't want to use additional software (like iBackupBot) then you can find your photos in the ~/Library/Application Support/MobileSync/Backup/[ID] folder of an old backup. The files have cryptic names and no file type, but your photos are all there - just hard to find. Sorting by size might help you get to the right files.
If you use some other backup method for your Mac, then use that to find and retrieve the old backup folder.
If you don't backup your Mac, or don't backup the MobileSync folder, then I am sorry to say you have lost them.
In future, I suggest you transfer all photos from the iPhone to your Mac using, for example, iCloud and Photo Stream.
Additional: No backup of Mac hard disk. Not all is lost - perhaps. In January your pictures were on your hard disk. Though they have since been deleted (by a more recent iTunes backup) at least some of the data which was you photo files is probably still there in the free space. This now getting well beyond the original question. Now we are talking about:
How to recover files which have been deleted from the hard disk. There are utilities which can help - for example Disk Drill. But, I think that should be new topic and that may get answers from those with recent experience of file recovery.
Best Answer
Here's the DIY method:
Navigate to the following directory:
~/Library/Application Support/MobileSync/Backup/
You'll get a cryptic list of folders. Inside each folder will be a large number of files with cryptic names.
Open these files in Quicktime Player.
There may be thousands of them but if you sort by size you should get video, audio and photos to float to the top.
Alternatively you could try one of the applications that is meant to do this such as iPhone Backup Extractor (There is a free and a paid version I have not tried either myself).