The idea is to take identity upside down: you issue your own identity (think key pair), and an authority certifies it (aka. signature). That's why it's called sovereign.
Adding zero knowledge proofs adds support for more privacy preserving tech: prove your address is in a specific country, without giving your address, or prove your age without giving your birthdate.
Although it could all be implemented today, governments don't... because they love centralisation for the power it gives them. European institutions are working on Sovereign Identity projects, but it's mostly 100% centralised bullshit from what I know.
As with all things cryptographic, if you don't own the keys, you own nothing.