Fl. is an abbreviation of the Latin verb flourit or floruit, meaning “to flourish”. What an art historian means is that the ‘artist flourished’. The often long dead artist had an exceptionally active period in which s(he) produced masterpieces. More broadly it can refer to the artist’s active years as opposed to date of birth and death, which can sometimes be meaningless in determining when art was executed.
Here is an example:
“fl 1345; d Venice, before 14 May 1389”
The artist work was in high demand by 1345, and the artist died in Venice before 14 may 1389.
Arguably Vincent van Gogh floruit in Arles, France, between February 1888 and May 1889, in which he produced 187 paintings widely considered his finest work.
