So I hope you don't mind if I give a second dimension to this massive multi-dimensional concept.
Agile as a mindset and a movement started out in the software development and delivery space. But my first brush with "agile" as a concept was when I was studying business management in South Africa around 2003. The South African management textbook that mentioned "agile companies" stated that the future of businesses relied on them becoming more agile to keep up with customer needs. Although this was after we had implemented much of eXtreme Programming (XP), it was still before (because South Africa has/had very slow internet connectivity, and expensive imported books were scarce) the big software movement really got going worldwide.
I reckon it is likely that the line in that South African management textbook had been inspired by The New New Product Development Game written by the great management scientists Hirotaka Takeuchi and Ikujiro Nonaka in 1986.
But skip to the here and now nutshell point:
Agile is now an umbrella term to mean all of the agile manifesto, agile principles, agile frameworks, agile practices, agile tools, agile approaches.
Basically, any abstract or tangible thing that helps an organisation or an individual, be quicker or nimbler, in delivering value to the end customer. Usually this begins with the mind/thinking framework being applied by the people to the challenges they're responding to.
In other words, it is more important to be agile, than to do agile. For more practical thoughts on agile checkout my collection of teaching/learning agile at What Is Agile For