There are many components which make up a complete fighter.  Components would include technique, accuracy, power, and speed.  But there is one component that is more important than these.  This component is flexibility.  Without flexibility, the other techniques could not reach their true potential.
Flexbility allows the body full range of motion allowing techniques to be executed freely.   Say your instructor wants you to perform a kick at waist level, but you do not have the flexbility to kick that high, you will fail to hit the midsection.  If you were to use all of your energy to exert that kick to the midsection and actually kick it, you will not have enough energy to generate power or speed, rendering it practically useless.  This is not to mention you could injure yourself doing it. But say your instructor asks you to kick the midsection, and you have the flexibility to kick at head level of a six foot four person, you will be able to generate energy to execute a powerful and fast kick to the body without any resistance.
There are a lot of ways to work on your flexibility.  You would perform stretching routines at the beginning and end of your workouts.  Make sure you do not stretch cold; warm up your muscles first.  Spend at least ten seconds or so at the beginning.  Focus on every part of your body; from arms down to your legs.  Put more emphasis where you will do most of your training such as your legs for kicking drills.  The stretching in the beginning will prepare your limbs for the extraneous exercises you will have to perform.
At the end of your workout, spend a good thirty seconds on each stretching exercise.  Stretching properly at the end of each workout will help reduce soreness, and it will improve your flexibility.
I want to share a little story about my experience with flexibility.  When I was a child, I had the worst flexibility you can imagine.  I could not stretch to ninety degrees.  But during my high school years and training in Ninjutsu, I was determined to perform the side splits.  By the end of my senior year, I was able to do the full side splits.
Every fighter should focus on their flexibility during every one of their workouts just as much as you focus on the other components.  Doing so will help you reach your ideal goal of being a great fighter.   Not doing so will just make you an easier target.