A Cinemagraph is a still image, with a small part moving or animated. They have been called "living images". The technique was first used in 2011 for news and fashion photographs, and is becoming more popular with the advent of autoplay on Facebook. They can be used on websites for eye-catching images.
The technique involves using a short video sequence from which a still image is extracted. Or the still image is taken in hi-res first, along with a video sequence. A short, 2-5 seconds, part of the video is then integrated into the still image. This part should seamlessly repeat, creating an interesting and eye-catching image.
They can be produced as gifs, which animate, or as short video sequences. Animated gifs will automatically play on your website, and on many social media sites.
For examples of cinemagraphs, do a search on the internet. There are some examples on http://derekphillipsphotography.co.uk/cinemagraph.html
By Derek Phillips of Derek Phillips Photography, Haverfordwest