Their official name is cinemagraphs. They are a mixture of photos and perfectly looping short videos seamlessly blended together. There is motion only in one part of the image, while the rest is still. The technology is not new, but in the past they were rendered as animated gifs, which were worked for vectors but not so well for videos and photos, which looked awful and were large and slow-rendering. Now we have moved beyond the old technology and, what stands out are the beautifully rendered HD video cinemagraphs.
Why would you want to use them?
They are a powerful way of conveying a message. It's always surprising to the audience that the photo is moving! It's alive! They can be used only in digital content. The shorter they are, the less bandwidth they use. Social networks like Instagram, Facebook, and Twitter support HD cinemagraphs and automatically loop the content. They make more sense when they are shorter. They can be as short as a few seconds depending on the moving part's complexity.