"Cinemagraphs are still images that contain within themselves living elements allowing a glimpse of time to be experienced and preserved. Cinemagraph is a technique of blending the effects of images and videos. It was introduced by a New York fashion photographer Jamie Beck, in collaboration with motion graphics designer Kevin Burg"
A far cry from the crude animated gifs common on the web in the 90's and early 21stC web, these examples examples demonstrate the scope and potential of this new medium I think what might be interesting for educators is the power to focus on, and highlight some hidden detail, a nuance that might be missed in a video or still image.
For example, what details would a geographer, a mathematician, or a linguist choose to emphasise?
This article also provides a useful guide on the technical aspects of making cinemagraphs. If you want to explore creating animated gifs on a mobile platform then there are some apps available including Giffer. Some more examples here.