Does it mean it lives in the official Rust repository, and is maintained by official Rust team members?
The nursery is a sort of semi-official repository. Code being in there doesn't necessarily mean it's better than a third party crate or even that it's better maintained.
It might be best to think of them as experiments by the Rust team. They might become part of Rust proper or become an important tool or they might just be a stepping stone for something else. And sometimes experiments fail.
Also note, the nursery is officially deprecated. New projects are no longer added to the nursery, and existing projects are supposed to move to other orgs. A lot of projects still live there currently, though, because there isn't a strong motivation to move them right away.
For details, see: