O.Henry is describing a millionaire's estate:
"The Millionaire's palace occupied a lordly space. In front of it was a lawn close-mowed as a South Ireland man's face two days after a shave. At one side of it, and fronting on another street was a pleasuance trimmed to a leaf, and the garage and stables."


Webster's 1913 Dictionary

Definition: \Pleas"ance\, n. [F. plaisance. See {Please}.]
1. Pleasure; merriment; gayety; delight; kindness. [Archaic]
--Shak. ``Full great pleasance.'' --Chaucer. ``A realm of
pleasance.'' --Tennyson.

2. A secluded part of a garden. [Archaic]

The pleasances of old Elizabethan houses. --Ruskin.



I assume that "pleasuance" in the text is a typo.