The old Persian word 'paradise' means 'wall around' and was originally used to describe a hunting park.
The walled enclosures were then used as reserves for exotic plants and exotic animals. They were amongst the booty brought back from military expeditions.
It is likely that palaces were then located inside hunting parks and smaller walled encosures were made for the kings residence and his orchards. This too was known as a paradise and one can still see Persian gardens with mud walls enclosing orchards and flowers. They also have networks of small canals which functioned as a water supply as well as an ornamental feature. This combination became known as a 'paradise garden': a walled enclosure with plants, birds, fruit trees and geometrical canals.
Note: The word 'paradise' took on its present meaning ('heaven') when it was adopted by the Greeks. The garden then became a symbol of heaven in the Abrahamic religions (Judaism, Christianity and Islam).