An icon is not, in the tradition that makes them, simply religious art. It is theology in line and color — a window, as the tradition says, onto the persons it depicts. Iconographers speak of 'writing' an icon rather than painting it, because the work is understood as a kind of proclamation.
Whether icons could rightly be made and honored was the question of the iconoclast controversy, settled for the East at the Second Council of Nicaea in 787. The council drew a careful distinction: the veneration shown to an icon is not the worship due to God alone, and the honor shown to the image passes to the one it represents. The defense rested on the Incarnation — because God had truly become visible in Christ, he could be depicted.
The icon is central to Eastern Orthodox worship and life, and is honored in the Roman Catholic tradition as well. Many Protestant traditions, reading the commandment and the role of images differently, do not use icons — a difference described, descriptively, on the relevant tradition pages.