Twitter has introduced a new feature called mute for its Android and iPhone apps; and Twitter.com. This new feature lets you mute your least favorite users on the service. This means that on muting a user, their Tweets and Retweets will not be visible in your timeline, and you will not receive push or SMS notifications from that user. On the other hand, the muted user will not know that you have muted them and still be able to fave, reply to, and retweet your Tweets, but you won’t see any of that activity in your timeline. You can unmute, the muted user at any time.
To mute someone from their profile page on Android, iOS, or Web, simply tap the gear icon on the page and choose “mute @username.” To do the same directly from a tweet, tap “more” and then “mute @username.” Don’t worry if you are not seeing this option yet, as the new feature is rolling out gradually.
SOURCE: Twitter Blog