It solves ownership of data, and removes the need for large data centers by securely, anonymously letting users share storage space.
I'd caveat that we're still in alpha, but things are coming together very nicely.
The Safe Network (will) incentive user storage and uptime through cryptocurrency, though non-blockchain based, so avoiding a lot of throughput pitfalls there. So it can also act as a storage backed currency in some fashion.
It allows users to truly own and manage the permissions of their data without relying on any third party. And it provides enough flexibility for this to let folk make applications as well as store files.
I hope that helps some? I'm trying to avoid buzzwords :) I know that site has any. It's also worth noting that the dev hub is a bit out of date (things are still moving pretty fast.) But the community (https://safenetforum.org/) is very friendly!
Let me know if I can get more specific, I'll be about for a little longer.
(Oh, also there's some other links in another top level post I made that may be helpful)