Both color and timbre are measures of similarity. Songs with the same color/timbre can be expected to sound somewhat similar. While timbre only takes contains information on how a songs sounds (e.g. in terms of instrumentation), color also contains rhythmic informations.
After you analyzed for color (timbre is not really important in beaTunes 5 anymore), results for functions like "Play similar songs" (in the context menu) lead to much better results, as beaTunes uses the color information (among other things) to determine, what exactly is "similar".
You can also take advantage of color when using matchlists. Those are lists that can be created by beaTunes based on your own ruleset (specified in the prefs). To those rulesets you can add a color rule, which basically means that you want to find songs that have a similar color as the template song.