What is a tone monster? He or she is a person whose playing is defined by their tone. They are the musicians you can recognize after only a few notes. Many players who are learning get caught up in trying to play fast, or trying to cram 1000 notes into every solo. But, what does a few well-placed notes sound like? Sure, it's great to have the chops to play whatever you want, but it's that rich sound that I'm after, more than anything.
How do you sound like a million bucks? Is it the instrument? The hands? The mind? The ears? In my opinion, it's a little bit of all those things. I'd suggest having a "tone model:" a player you love to listen to. Soak up recordings by that person; hear them play in person. Let their sound become deeply imbedded in your subconscious. Let that be the sound you are striving for. It may involve a different instrument, but just as likely, small adjustments to the way you play will yield just as great of results. Experimenting with picks, pick angle, distance from the bridge, etc all have a huge impact on your sound. Tone is 95% in the right hand.
You'll never sound exactly like another player, but the journey to copy another player's tone that will help make you sound better, and ultimately help you sound more like "you."
Andy's tone models on mandolin are Adam Steffy, David Grisman, Butch Baldassari, and Dempsey Young. Who are yours?