While the feature is still rolling out to all users today, a small group of users might also notice that when replying to a tweet, the @names at the beginning will no longer affect the number of characters remaining. (But it's still unclear for now whether you'll be able to keep adding on usernames until you eventually build a never-ending Twitter canoe.) As part of this trial run, Twitter is also testing a way to get rid of the ".@" convention, so that tweets beginning with an @username will be broadcast to all followers, rather than behaving like a reply.
If you're tweeting through one of Twitter's official apps, the usernames you are replying to will appear in the heading of your compose window instead of being listed in the body of your Tweet. So, if you're using an outdated app, Twitter says tweets might look a little weird or cut off for awhile. Finally, there's no word yet on that rumored feature allowing users to attach longer text blocks or, you know, more useful anti-troll tools.
Update: This post has been updated to clarify some of the new @-reply behaviors and tests.