The still photograph with motion
A Cinemagraph is a still photograph that has a small element that moves normally repeating. These images are starting to appear every where in TV advertising, TV programme trailers and Video Bill boards etc.
You can make them using a series of photographs and animating them, or use a video clip.
The easiest way is the video clip, most DSLRs will shoot good quality video all the way down to the mobile phone.
All you need is a video clip with some kind of action that will repeat and look natural when seen as a looped video clip of around five or six seconds duration.