In the upcoming version of Photoshop there is a feature called Content-Aware fill.
This feature will fill a selection of an image based on the surrounding image - to the
I'm guessing that for the smaller holes they are grabbing similarly textured patches surrounding the area to fill it in. This is described in a paper entitled "PatchMatch: A Randomized Correspondence Algorithm for Structural Image Editing" by Connelly Barnes and others in SIGGRAPH 2009. For larger holes they can exploit a large database of pictures with similar global statistics or texture, as describe in "Scene Completion Using Millions of Photographs". If they somehow could fused the two together I think it should work like in the video.