To explain what a rendering intent is, it is necessary to consider the function of a colour profile, it converts from one colour space to another.
I explained that different colour spaces have different sizes - they can print/show a different range of colours. RGB devices can usually produce a greater range of colours than a CMYK device because CMYK starts with paper-white and filters it, therefore it can't improve paper-white. RGB devices can always glow brighter.
If we have a nice bright RGB colour, it is quite possible that it can't be represented in a CMYK colour space. In plain English, your monitor will show a colour that your printer can't print.
So what should the computer do with that colour? You have a choice and that choice is controlled by the rendering intent. That choice depends upon what you are printing and how you want it to look.
Let us assume that the colour is a company logo. I want to print the exact colour, if I can't print the exact colour then as near as I can get it. I want colours inside my colour space to be as close as possible to the equivalent. Therefore I choose a colorimetric rendering intent, keep in-gamut colours exact and move the colours that are outside the gamut to the nearest equivalent. There is an absolute and a relative colorimetric rendering intent. They differ in that absolute uses a theoretical white point whereas relative uses your paper colour, relative is the usual proofing intent.
There can't be anything wrong with that could there? Well not for corporate logos but consider a photograph.
Let's consider a photograph with a saturated area of colour, outside the colour gamut of a CMYK printer. It may be a colourful pink dress with lots of colour, folds, subtle nuances. If we use a relative colorimetric rendering intent to convert this image to a CMYK colour space the computer will move each out-of-gamut colour to the nearest equivalent, unfortunately for all those subtle pink tints, the nearest equivalent will be the same colour. The dress, with it's shades and nuances, will be printed as a flat block of colour. That's bad.
Perceptual rendering values colour differences over absolute colour values. That is to say that it's better to have a less pink dress with nuances than a nearest pink dress which shows a flat colour. Perceptual rendering takes the larger gamut and squashes it into the smaller one. All colours are changed, even those within the gamut so it is not ideal for logos but much better for photographs.
