Solid is a specification that allows for decentralized data storage in so-called pods. The idea is that consumer applications don't store a copy of your information in their own silo - thereby having many copies of your data floating around with 3rd parties - but instead query your pod. That's the ownership / self-control aspect of the idea.

The crux is that you can self-host your own solid server with your own pods, or choose to rely on a hosting provider. That's the decentralized aspect of the idea.

The big question is how this plugs into an economic model with real world incentives, interests, distribution of power / leverage, trust / credit, and so on.