GIFs have finally come to Twitter. On Twitter's website as well as its iOS and Android apps, you'll be able to watch a GIF in your timeline by clicking a play button that shows up over top of them. GIFs won't animate automatically, likely to prevent you from downloading large files that you don't need. Opening up a tweet on its own will, however, immediately begin playing the GIF.
Support for GIFs has been a highly requested feature, and adding it in makes reading through a Twitter feed much simpler, as you won't have to open up a new window every time you want to view one. Notably, Facebook has adamantly refused to add support for GIFs, seemingly over concerns of how it would make its News Feed look. They may not all be beautiful, but Twitter seems to get that they're all fun.