Later this week, Twitter introduced a new Mute feature for people who use iPhone and Android apps and the web twitter.com. The Mute feature gives you even more control over the content you see on Twitter by letting you remove a user’s content from key parts of your Twitter experience.
This feature can be very useful when a person you're following begins rapid-fire tweeting from an event you have no interest in, or is engaged in a protracted public conversation that you'd rather not participate in. The feature will also be a helpful for many businesspeople who use the service, as it allows you to pay someone you've networked with the courtesy of a follow on Twitter, even if you'd rather not consume the content in their Twitter stream.
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 his/her profile page, tap the gear icon on the page and choose mute @username.
Till date, the feature is not available for everyone. Twitter will roll out this update in coming weeks.
Source: Twitter Blog