Cinemagraph
Cinemagraph sometimes called cinegraph are (quoted from wikipedia): still photographs in which a minor and repeated movement occurs.
This image is from here and belong to its author.
The moving part is normally contrasting with the stillness of the rest of the image, this is why most, the description is talking about minor movement.
This phenomenon has become quite popular lately, and can be absolutely mesmerizing when correctly done.
They are mostly distributed in gif, gif always play in loops, but a cinemagraph should be made so the loop point is almost unnoticeable.
If you like this, you can jump into it: