What is Gutenberg?
Gutenberg is the future of web publishing with WordPress. It will completely change the way you create content natively with WordPress now. You will be introduced to a new thing called "Blocks". You will be able to create your content using different blocks, such as headline, paragraph, image, gallery, etc..
The project has been started in June 2017 and since then is being actively developed. Currently, it is available as a feature plugin and is in beta/testing phase. You can directly install it into your WordPress website and play around with it. Remember it's not ready yet to run on a live/production website. But you should start exploring it and get used to of how it works and pass your feedback to the development team to help the project.
It is expected to ship with WordPress 5.0 sometime in April 2018 (as per Matt's estimation). Gutenberg will replace the current editor entirely (you may keep the classic editor active with this plugin).