Casey Newton, writing at The Verge:
One of the most-requested features for Twitter's mobile apps may be on the cusp of arriving. Some users of the company's iOS and Android clients are now seeing an option to mute accounts that they follow, preventing another user's tweets and retweets from appearing in their timeline. The user remains muted until you manually unmute them. In essence, then, the mute feature works as a kind of stealth unfollow — you won't be seeing another person's tweets, but they won't know that.
Alongside timeline sync and streaming, mute is one of the most popular features of third-party iOS clients such as Tweetbot and Twitterrific. Based on screenshots from people who can see the feature in their Twitter app, it looks like Twitter is experimenting with a simple account-based option; in Tweetbot, you can create complex mute filters for keywords and usernames.
While I don't see myself moving away from Tweetbot 3 any time soon, I'd certainly welcome a mute button in Twitter for iOS (which I like to use when looking for news).