I actually don't think it's that hard to grasp, but people often don't explain it very clearly.
It's a from the ground up design for a serverless p2p 'overlay' operating system.
Overlay just means that you run an Urbit VM on top of a mac/linux OS and people can write applications for your Urbit VM. Your Urbit VM communicates with other Urbit VMs in such a way that the application design is p2p by default so the complexity of this is hidden from the user. This means in the future someone can start up their urbit node (which will just look like another application) and use the apps in it without needing any central servers.
Right now the main app in their release is chat, they also have a link aggregator app too.
The reason for the finite user IDs is because the founder believed that one reason for service centralization on the existing internet was the spam problem. When IDs are free people can make tons of them and spam others, complex algorithms via centralized services are required to fight this which leads to a client/server model and a handful of enormous corporations powering the services.
When you have a small cost on the ID you make it economically infeasible to spam people, you also make it easier to stop IDs from abusing the network (and other people). It’s also a way to incentivize people to run infrastructure nodes in the network.
The other interesting details are that it's written in its own functional language on top of its own functional like assembly. This has benefits around correctness that I don't totally understand - but the idea is if you were to redesign a modern computing system from first principles taking everything learned over the last 50 years how would you do it?
Regular users are never going to run their own linux servers to host their own applications on the modern internet, but regular users might use an application that is p2p by default and does the things they want. This leads to a better decentralized model at the application level that is not ad supported.
Ultimately it's out of the box private servers that you can run locally and easily share data between securely, without the need for a centralized company in the middle.
The project makes me think of Alan Kay when he talks about big ideas and 'having the chops' to implement them. It's crazy to throw away most of modern computing and build a functional OS from scratch in a radical kind of way, it's crazy for the product to have made progress since something like 2002 (picked up a lot when they got funding more recently) rather than fizzling out or being vaporware. I'm amazed that they have real software shipping that works, but they do. It's a project driven by a clear vision of how computing can be better than it is, which I think is an exciting thing.