"Freestyle is a style of hip hop where an artist writes an unreleased verse, with or without instrumental beats, in which lyrics are recited with no particular subject or structure.[1][2][3][4][5] It is similar to other improvisational music, such as jazz,[6] where a lead instrumentalist acts as an improviser with a supporting band providing a beat. Freestyle originally was simply verse that is free of style, written rhymes that do not follow a specific subject matter, or predetermined cadence. The newer style with the improvisation grew popular starting in the early 1990s. It is now mainly associated with hip hop.

Original definition
In the book How to Rap, Big Daddy Kane and Myka 9 note that originally a freestyle was a spit on no particular subject – Big Daddy Kane said, "in the '80s, when we said we wrote a freestyle rap, that meant that it was a rhyme that you wrote that was free of style... it's basically a rhyme just bragging about yourself."[7] Myka 9 adds, "back in the day, freestyle was bust[ing] a rhyme about any random thing, and it was a written rhyme or something memorized".[6]"

References
Kevin Fitzgerald (director), Freestyle: The Art of Rhyme, Bowery, 2000.
T-Love, "The Freestyle", in Brian Cross, It's Not About A Salary..., New York: Verso, 1993.
Gwendolyn D. Pough, 2004, Check It While I Wreck It, UPNE, p.224
Murray Forman, Mark Anthony Neil, 2004, That's The Joint!, Routledge, p.196
Raquel Z. Rivera, 2003, New York Ricans From The Hip-Hop Zone, Palgrave Macmillan, p. 88
Edwards 2009, p. 182.