"The Sally Gardens (reel)", in Gaelic "Na Garranta Sailí" is a well-known reel. It is not related to the song also known as "The Sally Gardens".
Salley or sally comes from the Latin name ‘salix’ or ‘salyx’, meaning willow (‘aspirin’, or acetylsalicylic acid, was developed from an investigation of the folk remedy of chewing willow shoots to relieve pain), or from the Gaelic word for the plant, "sailleach” (which itself may have been derived from the Latin). The Salley Gardens therefore simply means willow gardens which were kept for medicinal purposes near villages and towns.
It has been recorded by Grey Larsen, Mick Moloney, Eugene O’Donnell, Michael Cooney, James Galway and the Chieftains, Planxty and others.
I don't remember where I learned it.