A picture [please note 'picture', not 'photograph'], in order to be memorable, should 'say' something. As an example, a fine portrait should enable someone who doesn't know the subject to learn something about him/her. It 'says' something about the person. The stunning photograph of the judge in Steichen's 'The Family of Man' comes to mind.
Be it a landscape saying 'Here is nature in the raw', a portrait saying 'She has a great sense of humor', a flower saying 'Isn't this beautiful?' or an abstract print remarking on the interrelationship of its elements, the composition is important to the extent that it presents the 'message' in a focussed [pun intended] and forceful manner.
In short, composition is a means to an end.