Facebook Messenger is the stand-alone app used by mobile devices for chatting with friends on Facebook. It was first published as an optional app, but Facebook in mid-2014 made it mandatory for using its chat service on phones and tablets — no more chatting from within the Facebook proper app.
The Facebook Messenger app has been hit with a bit of misguided criticism over the permissions it requires, starting with a poorly written Huffington Post article in December 2013. That outdated (and not so good in the first place) story gained traction as the Messenger app became mandatory. But as Android Central showed in its detailed look at the permissions, it's not doing anything that you wouldn't expect from a chat client. Apps such as Google Hangouts share many of the same permissions.