Motion Photos do exactly what the name suggests: They capture frames before and after your image, so your picture appears to be moving. Previously, users had two options: "Save as still photo" or "Save as video." But now, if you open the "Export" menu, "Export as GIF" is a third option.
The resulting file size isn't exactly optimized for the internet: 9to5Google reports that their attempt netted them a 28 MB GIF. But they did note that the quality was quite good, with a resolution of 768 x 1024. Presumably you could use one of the many ubiquitous internet app to trim the file size and optimize it for sharing.