Perceptual
Compresses the total gamut from one device’s color space into the gamut of another device’s color space when one or more colors in the original image is out of the gamut of the destination color space. This preserves the visual relationship between colors by shrinking the entire color space and shifting all colors – including those that were in gamut.

Saturation
Reproduces the original image color saturation (vividness) when converting into the target device’s color space. In this approach, the relative saturation of colors is maintained from gamut to gamut. This render intent is primarily designed for business graphics, where the exact relationship between colors (such as in a photographic image) is not as important as are bright saturated colors.

Relative Colorimetric
When a color in the current color space is out of gamut in the target color space, it is mapped to the closest possible color within the gamut of the target color space, while colors that are in gamut are not affected. Only the colors that fall outside of the destination gamut are changed.

Absolute Colorimetric
Colors match exactly with no adjustment made for white point or black point that would alter the image’s brightness. Absolute colorimetric is valuable for rendering “signature colors,” those colors that are highly identified with a commercial product such as the yellow used by the Eastman Kodak Company, or the red used by the Coca-Cola Company.

Taken from Adobe's CustomerFirst Support document for color management in Photoshop 5.