What is Agile?

Agile is an iterative and incremental (evolutionary) approach to software development
which is performed in a highly collaborative manner
with "just enough" ceremony
that produces high quality software
which meets the changing needs of its stakeholders.
Scott W. Ambler

“a set of techniques and procedures with minimal overhead that allow us to make sound, just-in-time decisions.”
Noel Llopis (with a set of very interesting visualisations)

and, of course:

agile vs. Agile