Imagine I am designing my business card, and i "intend" to "output" my Black and White image on green paper. Now, you would not want to actually send a PDF with that green tint built into the background of the card, but if you wanted to see if your head shot was light enough to 'visually work' on that green paper, you need a method to both "simulate' this on screen - and also "proof' it on some paper (even if you do not have any green paper)
This would be an extreme example of a PDF/X "output Intent"
and - you need a way to give someone the art without the green tint in the art, as well as a way to communicate 'what you intended the output to look like" - aka - 'output intent'
