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An icon theme is a set of icons that share a common look and feel. The user can then select the icon theme that they want to use, and all apps use icons from the theme. The initial user of icon themes is the icon field of the desktop file specification, but in the future it can have other uses (such as mimetype icons).
From a programmer perspective an icon theme is just a mapping. Given a set of directories to look for icons in and a theme name it maps from icon name and nominal icon size to an icon filename.