From the Store description for v220.127.116.11:
Transfer My Data is a quick and easy way of copying contacts from almost any phone (Symbian, Android, iOS, BlackBerry, Windows Phone and others) to your new Windows Phone using Bluetooth. Some phones may also be capable of transferring text messages and pictures, including many Lumia phones. Transfer my Data copies all your contacts into the Windows Phone People Hub, from where it’s easy to call, mail, chat or follow friends on your favourite social network. On supported phones, contacts and messages can also be transferred to and from an SD card.
- Transferring text and MMS messages to and from an SD card
- Bug fixes
The core functionality is unchanged, other than the bug fixes, while the SD card functions are tucked away, completely out of sight, on the '...' menu. The inclusion is somewhat odd, but I guess backing up contacts and SMS does come under the general title of 'transferring data', so why not?
The use case is presumably to aid transferring this information locally - the exported files are in .vcf format - pretty standard for contacts - and .vmsg format - which I'd never heard of - for SMS and MMS. It does seem as though there are ways of getting the latter onto other phones, but none are trivial.
Still, more ways to backup are always good. Here are some screens of the new Transfer My Data in action: