Many organizations allocate people and/or time to maintain presence on Twitter. Here are some measurements that can be used to measure the effectiveness of those efforts, along with some tools that can help gather those numbers.
Audience = Number of users following a Twitter account (metric: followers)
Retweet prostpect = Number tweets containing "RT @user" / Number of tweets sent by @user (metric: percent)
Site Twitter appeal = Number of links from tweets to a site during one day