Twangyness or twanging of pitches is the individual colour that each individual pitch has. Twangynes of pitches is on of the things that makes tuning the guitar difficult.
The color is the individuality of tone that people that has absolute or perfect pitch talk about.
Our brain works from the general to the individual. Like the leaves on a particular three, everyone of them is different and has its own individuality or personality, so to speak. So too with pitches in musical instruments. First when you start to listen to a pitch, you are not acutely aware of the individuality. You have to listen, really listening to each and every note to really get to know it personally.
If you're not aquainted with twangyness of pitches, then try to sing different vocals (letters from the alphabet) and try to hold the tone in the same pitch. For instance, sing aaaaaaaaooooooouuuuuuyyyyyyyeeeeeeiiiiiii. Try with more and less closed mouth. Listen to the overtones that is introduced and the changing colors of your voice, and the changing overtones. Then try to hear the same phenomenon in individual pitches on your guitar. Listen to how the sound often continuosly changes, and is never the same. You will find that there are some pitches that are more solid and unchanging, less twangy, then others, and if you listen to this a lot, you will find that every note has .