I have worked in the print industry for over 6 years and am amazed when people ask me what relative and absolute mean. Im going to give an explanation for what they do and how they work when converting colour profiles ready for print.
Rendering intent mainly tells the CMM how to deal with “out of gamut” colours; colours that exist in the source space but cannot be coded directly into the destination. Depending on the intent chosen, some in gamut colours are usually affected also. It should be noted that when converting into any of the currently used “editing” colour spaces such as sRGB, Adobe 98, ProPhoto etc., the only intent currently supported is relative colorimetric. Photoshop CS1 and earlier allowed absolute colourimetric as well, but this was rarely a useful option. Adobe decided that absolute was being chosen by mistake most of the time that it was used and discontinued the option for CS2 and later. So while the other rendering intent choices show up in the menu for these spaces, if you choose one of them and click the preview box you will see that they have no effect.
Perceptual maps all possible colours (from LAB- it knows nothing about the size of your source profile) to in gamut ones while maintaining smooth transitions to the colours that would have been in gamut any way. This has the advantage of preserving smooth transitions and maintaining relative colour relationships, but tends to affect a more significant amount of in gamut colour than the other intents. It is widely used for photographic images, where relative colour relationships are often more important than absolute colour accuracy. To maintain the relationship between in and out of gamut colours however, severe compression is applied to almost all colour values, including in gamut ones. This means that some saturated colours that could be reproduced in the destination get somewhat de-saturated. This happens even when no colours in the source would be out of gamut.
Relative colourimetric attempts to leave all in gamut colours unchanged, and map out of gamut colours to the nearest in gamut choice. This makes it an excellent choice if all of the source colours exist in the destination space. If this is not the case however, then the transition to the formerly out of gamut colours can be abrupt. A whole range of out of gamut colour may be translated to the single nearest destination colour. We call this “saturation clipping” because the end points of a colour range are clipped off, or stop becoming more saturated. This changes the relationships between colours and in extreme cases can lead to flat blobs of saturated colours where a gradation would otherwise be. Sometimes this is objectionable, other times it is hardly noticeable.
Absolute is similar to relative colourimetric in that it preserves in gamut colours and clips those out of gamut, but they differ in how each handles the white point. The white point is the location of the purest and lightest white in a colour space. If one were to draw a line between the white and black points, this would pass through the most neutral colours.
Absolute colourimetric preserves the white point, while relative colorimetric actually displaces the colours so that the old white point aligns with the new one (while still retaining the colours’ relative positions). The exact preservation of colours may sound appealing, however relative colourimetric adjusts the white point for a reason. Without this adjustment, absolute colourimetric results in unsightly image colour shifts, and is thus rarely of interest to photographers.
This colour shift results because the white point of the colour space usually needs to align with that of the light source or paper tint used. If one were printing to a colour space for paper with a bluish tint, absolute colourimetric would ignore this tint change. Relative colourimetric would compensate colours to account for the fact that the whitest and lightest point has a tint of blue.