A cinemagraph is basically a combination of a static photograph with either video or sequence of images. It gives the impression of being a video, but not quite.

They are commonly produced by taking a series of photographs or a video recording, and, using image editing software, compositing the photographs or the video frames into a seamless loop of sequential frames, often using the animated GIF file.

Images are taken from http://cinemagraphs.com. Please view the website as they have a few sets of Cinemagraphs that you can view.