Facebook is bringing real-time location sharing to Messenger so that users will have the ability to let those they're chatting with know where they are at any given time during the conversation. If for instance you're meeting someone for dinner then you can tell the person where you're at, or rather show them, by tapping on the location button. You can find this in the overflow menu that sits at the bottom of a chat at the end of the list of other actions, so it won't be right out there in the open for you to tap. That being said it isn't really all that hard to find either which is a good thing as this seems to be a big feature add for Facebook.
According to Messenger's Head of Product Stan Chudnovsky, people are often asking each other in chats of their whereabouts so they know how far away they might be when on the way to a meetup. This kind of information displays that people are constantly asking a question that could be answered by someone listing off a time frame that guesstimates their ETA, but a more efficient way of doing things would be to give them the ability to share real-time location data. Not only does this give the other person a chance to actually see where you are, but since they would now know your location in real-time, they can formulate their own idea of how long you'll be before you show up, and this could save you from stating a time, then potentially missing that time. Additionally they can continue to check your location so they know where you are until you arrive.
More to the point, it's a smart move by Facebook and the Messenger team as Google just recently announced that they were adding the ability for users to share real-time location data via Google Maps. Google's new location sharing adds features like setting a designated amount of time for how long the location can be shared, and you can also share your location with just one person if you don't want to share it with everyone. With Messenger's new location sharing feature it isn't too much different though the amount of time is automatically set to 60 minutes once the location has been shared with another user. Location sharing is also optional so users won't automatically be sharing their location unless they choose to, and if they do share their location they can also hit a button to stop sharing it at any point. The feature should be rolling out to users in Messenger as of today, though Facebook doesn't seem to have given an exact time frame on how long it will take all users to see the change.