To fianchetto is to develop a bishop on one of the long diagonals, at b2/g2 (for white) or b7/g7 (for black).
The fianchetto is a term for the development of a bishop to the second rank of the adjacent knight's file, after having moved the knight's pawn one or two spaces. The main idea behind such a development of the bishop is that it is placed on one of the longest diagonals on the board, potentially increasing its scope/activity, and it can increase central control by surveying two key squares (either e4 and d5, or d4 and e5).