The best musicians in the world were not just born with talent -- they practice.  Long and hard.  Yes, some people are born with a natural talent for music, but if they do not develop and refine their talent with lots of practice, they will never realize their full potential.

Often, I see students get burned out on practicing.  Let's face it: practice is not always the most thrilling of activities.  It takes discipline.  Any accomplishment you achieve in life will take discipline. 
It's a lot like exercise.  You know the benefits of exercise -- looking and feeling great -- but exercise is not always fun.  Yes, you may love to get outside and play a game of basketball with friends, but friends are not always around.

The key is to constantly challenge YOURSELF.  Set goals for yourself -- small enough to make them attainable, and often enough to set you on a course for achievement.  You must own the goal-setting process, though -- your teacher can only help.  If you are not motivated to set your own goals, you will not have fun during the hours of practice that it takes to improve your skills -- or worse, you simply won't practice. 

Playing music is one of the great joys of my life, and even as a professional, I still challenge myself with new goals.  Because as difficult as a goal may be to achieve, nothing beats the feeling of actually accomplishing it.