The animated GIF has seen a resurgence lately among many sites and social networks, but they're still not all that easy to create. GIF Camera for Android makes it a little easier by allowing you to create a short animated image out of a series of photos, or by taking a video with your phone's camera.
It's not as robust as using Photoshop, but for casual use, this app should do just fine. You can use up to 20 frames, which isn't much, but it will still get you a second or two. Once the GIF is created it, will be stored in the Gallery, just like any other picture, whereupon you can share it via your preferred medium.
GIF Camera (free) [Google Play]