As far as technical definitions go, agility is the antipole of formality along a methodological dimension. Specifically, agility is "low formality", where by formality we mean high level of control, extensive documentation, and heavy bureaucracy.
Note that the agile-formal dimension is orthogonal to the process models, such that we can have agile waterfall, agile iterative, etc. just as we can have formal waterfall, formal iterative, etc. (Corollary: there is no such thing as agile vs. waterfall!)
Note that the agile-formal dimension is also orthogonal to the cowboy-disciplined dimension, such that we can be agile or formal, still we are required to be disciplined. (Indeed, this was the greatest achievement with agility, that before it we only had "cowboy" vs formal!)