Fibonacci lived during the time period known as the High Middle Ages where Europe had come out of the dark ages and was progressing on many levels. Political, economic, academic (mathematics obviously!), and social gains were all being made. Specifically in Italy the Byzantine Empire was finally forced out, and many of the Italian states either were or were working towards their independence.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html
Sources
O'Connor, J. J. "Leonardo Pisano Fibonacci." Fibonacci Biography. N.p., n.d. Web. 27 Feb. 2014.
O'Neill, Christopher. "Fibonacci." Fibonacci. N.p., n.d. Web. 27 Feb. 2014.
"The High Middle Ages." The High Middle Ages. N.p., n.d. Web. 26 Apr. 2014.