Twitter has officially rolled out a ‘mute’ button across official clients and the website, according to the Twitter blog. Muting a user means you won’t see their tweets in your timeline, and no more notifications. A muted user can still retweet or reply or favorite your tweets, you just won’t know about it. This lasts as long as the user is muted, it can be undone at any time.
You...you don't talk so much
From the post:
To mute a user from a Tweet on your iOS or Android device or on Twitter for web tap more and then mute @username. To mute someone from their profile page, tap the gear icon on the page and choose mute @username.
Due to the number of Twitter users, this is a phased rollout, so if you don't see the option on your account yet, be patient and it should be sowing up soon.