Sometimes you just don't want to hear everything people on your Twitter timeline are saying, especially if you follow a lot of accounts. Also, some people just get annoying. This is why third-party Twitter clients have long included muting. Now Twitter itself is embracing the idea with official support coming to its apps and website.
Users of the official Android (and iPhone) app will be getting the mute feature over the next few weeks. To mute a person, just hit the 'More' item on Tweets and select mute. You can also mute people from their profiles by tapping the gear icon and choosing mute. It's a similar deal in the web interface. This prevents all that user's tweets, retweets, and replies from appearing in your timeline. It can be turned off at any time.
Third-party clients have expanded mute features to include things like hashtags and key words, but Twitter is starting out slow. Still, it's a fine alternative to unfollowing people and bruising egos.