In short
In short: sovereign AI means you know and choose where your data is physically processed and who controls the compute the model runs on. The term appeared because nearly all the world's compute infrastructure sits with a handful of American companies. Europe answers with regional endpoints, where processing never leaves the continent, and with programmes for its own capacity.
Picture renting a warehouse in another country. The goods are yours, but once they pass through that door, the local laws, the local inspections and the local courts apply to them. Whose name is on the boxes makes no difference.
Computation works the same way. Send your client's text to a model and it is processed on a machine that sits somewhere. That somewhere decides who may demand access to it and by what procedure.
Which is why the word showed up in contracts before it showed up in headlines. A company handling sensitive data has to write down where that data is processed. The phrase wherever it lands does not go into a contract.
Sovereignty is not a flag on the server. It is the answer to whose court decides when something goes wrong.
How to check it
With one question to your provider: which region processes my requests, and can I put that in the contract. A clear answer is worth more than any privacy statement. A vague answer is also an answer.
Primary sources
European Commission: EuroHPC AI Factories (official)The visual is generated code-art, no third-party images.