The rendering intent is the pathway to get to the closest color the printer can print to the specified color in the file.
I notice a trend to place far too much emphasis upon rendering intents and their affects / effects for prints, especially in the case of earlier thread posts and mentions of white point, neutrals / grays, etc.
So far as sign makers are often concerned, rendering intents are useful to wrangle bright, vivid colors at the edges of the spectrum.
One can rather easily evaluate those effects by using Photoshop's Proof Colors feature. Try wild. Open the Onyx Quality Evaluation PDF using the common U.S. Web Coated (SWOP) v2 ICC profile while cycling custom soft proofing against the rendering intents.
Then, open the same file but using an ICC profile such as the EpsonWideCMYK_Ver2 as a start to the same exercise. One should easily see the significant difference between the two different ICC profiles and very little difference, if any, among rendering intents.
The EpsonWide ICC profile (like others available from machine makers) is somewhat that of the ProPhoto RGB ICC profile which is a very wide color gamut and where rendering intent effects may be noticed. Digital cameras especially can capture colors beyond the color gamut of color printing processes which may be stressed with pictures of bright flowers and the like of anything vivid but with subtle gradations. The effects of rendering intents can sometimes become readily apparent in such photographic images or artistic creations using the extremes of vivid colors. Maybe notice the bright yellow fruit pictured in the Onyx file. Recommended for photography is the Perceptual intent which will bring the most vivid colors into the most vivid capability of the printer / ink / media combination while preserving gradations. Using the Relative intent will likely lose some or all of vivid gradations.
Most often, it's hard to notice rendering intent effects in the vast majority of files.
So, the exercise should show that rendering intents play a rather rare part in the scheme of things but the initial input ICC profile is far more important.