On Twitter, replying to somebody can be a bit of a hassle, especially if they have a rather long handle. This is because the username of the person that you're replying to counts against the painfully tiny 140 characters that have defined Twitter for as long as most users can remember. When conversations spring from Tweets and involve multiple people, the landslide of Twitter handles can even result in there eventually being absolutely no room left for actual content, leading to the conversation going down the tubes entirely. Twitter is testing an update to fix all of that, and you may begin seeing replies that are the full 140 characters in length, or close to it.
A small subset of users, with the criteria thus far undisclosed save for the fact that they are only on iOS, is now able to Tweet a reply to another person, whether they're the original Tweeter or in mid-conversation, and not have the person's handle count against their character count. In order to help prevent the multi-user scenario mentioned above, this also works when replying to multiple people in a thread. Twitter did not say anything regarding Quote Tweets, however, which includes another person's Tweet as a media attachment in a more concise and public form of replying, allowing users to add commentary. This also means that, until further notice, Quote Tweeting yourself will have your username count against the Tweet limit.
With usernames out of the way, long-running conversations on Twitter will be much richer and cleaner, and conversations that end up in the public eye will have more insight to offer to those joining later on in the back and forth. The test is still being conducted on a limited basis on the replying user end, but all users will be able to see these extended replies if one from a tester ends up in their notifications or their feed. For now, Twitter has not announced any concrete dates as far as rolling out a wider test or taking the feature out of testing for public release. Given the fact that it's being given to random iOS users, it's probably pretty close to being ready for primetime.