Ever since it launched many years ago, the timeline you see on Twitter has been all about the reverse chronological order - you get the newest tweets at the top. This is set to change, however, following many rumors on the matter.
In the past Twitter brought you the "While you were away..." section, which was the first thing to ignore the reverse chronological order of tweets. And now the social network is taking that to the next level with the "show me the best tweets first" option.
This is rolling out "in the coming weeks". You'll be able to toggle it on and off through a dedicated item in Settings. When it's on, you'll see "the Tweets you're most likely to care about" at the top of your timeline after you've been away for a while. These will be "recent" and in reverse chronological order themselves - they just won't be the latest tweets. To get to those, you scroll down past the "best tweets" section, or just pull-to-refresh at any time.
Twitter says the new feature should create more and livelier conversations, as well as generally more tweets and retweets. When this becomes available for you, Twitter will put a notification in your timeline.