It's vague as hell though. Everybody from the agile consultants to the CEO down to the lowliest engineer projected their desires and intrinsic meaning on to the agile manifesto.
If you ask 10 people what agile "really" means you'll get 10 different answers, many quite incompatible with each other.
Agile focuses on the continuous improvement of not just the software, but the process. They tried to be specifically not too verbose, as dedication to one size and shape of process that does not fit all is precisely what they were against. Agile can be thought of as a meta-process. It's an attitude and a process for improving your process. Think kaizen for your software development team. It's about the tight feedback loop about what's working, what's not working, and what can be improved.
Beyond that, 10 people might find that the processes they've refined from Agile really do differ. That might be because of differing (and broken) application of Agile itself, which is a common claim. It might be, though, that continuous improvement of process has lead different teams in different directions that function well or well enough for those teams.
If you ask 10 people what agile "really" means you'll get 10 different answers, many quite incompatible with each other.