Ability of a business to quickly adapt to its changing environment.
It is hard to define the word “quickly” in the definition above. It is rather a relative notion depending on industry, market, geographical location and many other factors. However, in accounting terms, business is regarded as agile, when it responds to changes in its environment either fast enough (in case of business opportunities) to generate superior - compared to its competitors - profits or early enough (in case of business threats) in order to avoid the risk of losses altogether or minimize losses - again compared to its competitors - in case they are inevitable.
Therefore, being agile generally means being quicker then your competitors and hence having a competitive advantage.
Agility depends on a right mix of agile people, business processes and systems supporting them.¹
¹ IT system integrator - http://www.business-agility.com/ba_intro_whatwedo.aspx