The comments here are helping me figure out how it works, but it still leaves me with the question of what can I do with it that I can't accomplish with my good ol' OS or internet or (whatever the closest conventional analogue for Urbit is).
Any other peer to peer solution is partial, and therefore not able to compete with the internet as is. Urbit basically plans around an identity system that prevents spam and abuse; a hierarchical packet routing structure for those identities that doubles as a de facto governance model (due to having a vested interest in the network, the higher up you go); a kernel designed to freeze, and its entire OS on top a series of event logs that mark down computations and new states; a functional language for this "internet where every computer is a database", and the encrypted networking protocol that uses UDP while still ensuring packets always find you.
So if you wanted to, say, have a group of people set as a peer list that others can subscribe to or join, or build or use applications that lets that peer list join chats or see a set of files based upon some arbitrary marker (like giving you $5/mo?) ... you don't need a million services to spread the load, one task per service, each person joining each service. You can just use your own computer. It's a personal server platform for a peer to peer internet. It's an internet designed to resist bad actors, and to resist AOL, to resist Facebook and Google — an internet that facilitates and preserves a Usenet-esque model of small communities doing stuff together on their computers.
(Obvious disclosure that I work on the project, again.)
It also sounds similar to PGP’s web of trust model, which failed horribly. But you mention that you can get paid for renting out your resources. If you can somehow make that dream into a reality, then yes, it could be a big deal. Right now everyone tries to solve this partially: you can get paid to rent out your GPU (vast.ai) or your disk space (filecoin) but you seem to imply a more unified model, where payments can be continuous and effortless based on arbitrary metrics.
The whole “planet” and “galaxy” stuff is just confusing. Sure, metaphors are useful, but a basic explanation of the problem statement and the proposed solution would be better. Your explanation here has been the first time that someone put Urbit into terms that I could concretely go “okay, I see the point.”
It would help to have a condensed version of your comment on the website, as opposed to space metaphors and pictures of rocks ;)