There are plenty of services available that allow you to carry out private conversations across platforms. With today's announcement, Twitter makes it easier to serve as your messaging service.
Previously, direct messages were limited to the same 140 character limit as a public Tweet. Starting today, that limit has been lifted to 10,000 characters for direct messages. This should provide more than enough capacity for even the chattiest person.
Twitter made a few other changes to make private conversations easier back in April and this move is another way it is encouraging the use of DMs.
You may recall back in January 2015 Twitter also added support for direct messages for up to 20 people. Group support may be a great idea for project teams or to communicate with others on the road when you know they are on Twitter, but may not be connected in another service.
I use direct messaging a couple times a week, but feel a bit apprehensive about using a service where you could make a mistake and post something publicly that was meant for a private conversation. Do you use Twitter for carrying out private conversations? If not, do you use text messaging or another service?