in a widespread way
"oxidation ponds are extensively used for sewage treatment in the Midwest"
In an extensive manner, widely.
"The travel agency offers extensively documented guides that cover every corner of the country."
In plain English: Extensively means covering a very large area or dealing with something in great detail and depth.
"The company has extensively researched the market before launching its new product."
Extensively comes from combining the word extensive with the suffix -ly to form an adverb. The term entered English by attaching a common grammatical ending to describe something that is done over a wide area or in great detail.