The Oxford Online Dictionary
Noun: the cultivation of trees and shrubs.

Wikipedia
Arboriculture is the selection, planting, care, and removal of individual trees, shrubs, vines, and other perennial woody plants, and the study of how they grow and respond to cultural practices and the environment.

The Royal Forestry Society
The cultivation of trees to produce individual specimens of the greatest ornament, for shelter or any other primary purpose other than timber production.

Forest Research
Management of individual trees or groups of trees primarily for their amenity value.

The Arboricultural Association
Arboriculture - the production and management of trees and woody plants where amenity is a primary objective.