What exactly is colored sound?

Colorations occur due to:

1) the room in which playback occurs
2) frequency response errors which all loudspeakers have
3) incorrect interactions between amp and speaker which cause frequency response errors
4) distortion, which is found in all things electronic

It turns out that the ear is less sensitive to certain colorations and a lot more sensitive to others. For example the ear is not particularly sensitive to the 2nd harmonic (which is responsible for the coloration of 'warmth', often found in tube equipment) but is extremely sensitive (moreso than most test equipment) to the 7th (which is part of what causes harshness and a metallic quality and is why solid state has the coloration of 'bright' and 'hard' and the like).

Frequency response errors are also obvious colorations with multiple causes!

But its much more complex than that- the ear has tipping points where it will favor distortion over actual FR errors. Brightness in solid state is one example of that.

Digital and analog recording processes both have colorations associated with distortion and bandwidth, although in the digital world, the word 'aliasing' is used because digital guys don't like to admit that digital makes distortion (my 2 cents on that....).

Microphones also have colorations- as a recording engineer, I love my Neumann U67s which turn out fantastic results, but I'll be the first to concede that they aren't perfect by any means!

@tzh21y with so many sources and causes, it might be helpful to put this in a context as the topic is a bit broad. Did you have a specific area of interest?

One of the early Stereophile test CDs (the first one maybe) has a recording of J. Gordon Holt reading something with different mics swapped in every sentence or so. A great demonstration that should be heard by anybody wondering about recording coloration as it clearly and simply cuts to the chase. Flat SCHMLAT!

My best would be Muddy Waters. Extremely fine guitarist, best blues vocals, crazy womanizer. 

All sound is colored sound; none is precisely the same as what was recorded.

Again, before the recording itself there are microphones that cannot 'hear' as well as the ear. It goes from there. We should try to recreate in our listening rooms what ear would have heard not what microphones 'heard'. Of course, it's impossible. The closer the better.
One or maybe main reason why some hi-end systems don't really sound good - too far.  They can sound impressively but that's not how it sounds in reality.