Flurry is the English name of a pair of related but distinct positive status effects in Final Fantasy XI. Both have the same status icon as Haste and relate to making the target faster in some way.
The Flurry status bestowed by the Flurry and Flurry II spells is called Snap in Japanese (スナップ, sunappu?), and raises the Snapshot stat (which reduces ranged attack delay).
The other Flurry status is a rare random positive effect that occurs while investigating Nyzul Isle. It is called Flurry in Japanese (フラーリー, Furārī?), and has the same effect as Haste but stacks with it.