That only works because it found exact versions of that same picture on different websites and looked at the text of those sites and saw that the name "Barack Obama" was in the text of all those sites so it did an image search for "Barack Obama". Like I said: it searches for exact picture matches.
If you took your own picture of Obama that had never been posted online before and did a reverse image search, it wouldn't work.
Obviously it works better if it can find the exact image, but I don't think that's all that it's doing. For example, here's a picture of the Golden Gate bridge that I took myself from Angel Island, never before uploaded to the Internet:
It couldn't get the query, but it does get similar images, including at least one other that's also of the Golden Gate bridge. I unfortunately don't have any personal pictures of celebrities, but here's one of a slightly-askew photo of my computer screen that includes Obama's face (but deliberately not all of the original picture):
For the Obama one toward the bottom of the page there is the section "Pages that include matching images", so it did find the exact original image. I knew it would match even cropped images, but apparently it can also handle slight rotation and some color changes.
If you took your own picture of Obama that had never been posted online before and did a reverse image search, it wouldn't work.