Definition of Rendering Intent - Rendering intent describes the four modes by which color management systems adapt some or all colors in a picture to the limitations of a given display or printer.
From the Dry Creek Photo article on color management -
"For most images, Relative Colorimetric rendering produces superior results. For others, Perceptual will be far better. These cases include images with significant shadow details where a slight lightening of the print is acceptable to open up the shadows. Also images with areas of highly saturated color can benefit from Perceptual rendering. If you see color banding in the soft proof with Rel. Color. selected, try Perceptual. With experience you will get a feel for which images best pair with each rendering intent."
Intent Definitions - Per the Photoshop Print Dialog
Perceptual - Aims to preserve the visual relationship between color so it's perceived as natural to the human eye, even though the color values themselves may change. This intent is suitable for photographic images with out-of-gamut colors.
Relative Colorimetric - Compares the white of the source color space to that of the destination color space and shifts all color accordingly. Out-of-gamut colors are shifted to the closest reproducible color in the destination color space. Relative colorimetric preserves more of the original colors in an image than Perceptual.