You’ll see the option to follow country specific Moments, which will last throughout the Games, so the best of what’s happening with your team will appear in your timeline for the entirety of the Olympics. You can also just opt to follow your favorite sports and events to see these Tweets in your timeline, or catch up on what you missed every day with recap Moments that will highlight results, medal counts and more. Of course, when a Moment that you follow ends, so do the Tweets, leaving your timeline the way it was before.
I think Moments is the best feature Twitter has rolled out in years, and it's woefully underutilized by many people. It was a news story in the tech blogger community a few weeks back when people discovered that you can "subscribe" to a particular event in Moments and have top tweets related to that event show up in your timeline. This could be a game in the NBA Finals or an awards ceremony or a political debate, and it's a great way to follow something that you only care about sometimes.
Twitter is taking Moments further for the Olympics by allowing you to use Moments to more easily follow just the events you want to know about. It's a great use of the feature, and it may even get some Tweetbot and Twitterrific users to give the Twitter app a go.