USB Stick telling me to formatted needs to be done

Oh dear. Important material and files should always be backed up to a second storage device or to optical discs, and especially since USB drives are particularly prone to problems. I fear the files are lost.

What exactly went wrong though? How could a power outage damage a usb drive?

The most common damage is that partially-written data leaves the stick in an inconsistent state. If that is the case, there is lots of free software to attempt a recovery. DO NOT format the drive. http://www.tomsguide.com/us/pictures-story/332-free-dat...

Electrical damage is unlikely, but irrecoverable.

Your friend should learn a valuable lesson to back up her important data not only on one drive or storage device.
But, now, she should keep this USB drive free from any new data and select an efficient recovery tool to retrieve her data back online. Actually, it is not an easy task since there are plenty of recovery tools out there. So, I would personally recommend you to try a USB drive recovery freeware that has ever recovered 90% of my deleted data from a hard rive;

Important note: You should remind her to format her drive after the recovery process for saving this drive.
You should remind her to back up her important data on different drive or storage device in the future.

I tell everyone how important it is to back up important files, no one listens.

Thanks for the tips. I don't have high hopes in recovering anything.