If you have an iPhone 6s or 6s Plus, you can take a Live Photo, which is a still picture combined with a 3 second video captured 1.5 second before the still through 1.5 seconds after the still.
You can easily enable/disable Live Photo (there’s a control at the top center of the Camera app – tap it to turn Live Photo on and off), giving you better control over the extra memory that a Live Photo consumes.
Once you take a Live Photo, you can share it just as you would every other photo. If you share the photo using Messages, and if the recipient is running iOS 9, they’ll actually receive the Live Photo. To watch it, they first tap the photo in Messages, then tap and hold to watch the video.
Not every app supports Live Photos. For example, if you email a Live Photo, the email client will only send the still image and not the movie. This same is true if you try to post a Live Photo on Facebook, Twitter, etc. Note that El Capitan’s Messages application does not yet support Live Photos, but the Photos application does.
You can transfer Live Photos between iOS devices and Macs using AirDrop and iCloud Photo Sharing and you can also convert Live Photos into animated GIFs to share on social media. To learn more, read this article by Zac Hall and this article by Serenity Caldwell. Both are full of helpful details.