Twitter introduces Mute Button which is a new account feature and officially called as “Mute to People”. This new feature will allow its Android, iPhone and web client users to selectively turn off the posts of certain users they follow, without unfollowing them.
Muting a user on Twitter means their Tweets and Retweets will no longer be visible in your home timeline, and you will no longer receive push or SMS notifications from that user. The muted user will still be able to favorite, reply to and retweet your Tweets; you just won’t see any of that activity in your timeline. The muted user will not know that you have muted him/her, and of course you can unmute at any time.
To mute a user from a Tweet on your iOS or Android device or on Twitter for web, tap more and then mute @username. You can also mute someone from his/her Twitter profile page, to do that just tap on the gear icon on the page and choose mute @username.
It’s going to be rolling out starting today for everyone, and should be available to all over the next few weeks.
You can visit twitter support page to get more details at https://support.twitter.com/articles/20171399