The goal of Urbit is to make peer-to-peer software easy for developers to write and for users to run on their own. The code is completely open source, actively maintained, supported by a growing ecosystem, and used daily by thousands.
Urbit consists of two high-level components: an operating system (Urbit OS) and an identity system (Urbit ID). Urbit OS enables its user to communicate directly with others using Urbit OS via their Urbit ID's. You can think of these like phone numbers — meaningless but memorizable, and likely to identify the same person reliably through time.
Using Urbit requires having access to a running ship: an Urbit OS running with a supplied Urbit ID. You can run Urbit yourself if you're comfortable at a command-line or willing to learn. Otherwise you should probably use a hosting provider — that is, someone that provides you with an Urbit as a service.