When we were kids, we grew up with vivid imaginations.  Some of us were very creative and came up with great ideas.  Others had imaginary friends.  In whatever way we used our imaginations, we used them well.  Shadowboxing brings that imagination back.
Shadowboxing is a great added benefit to martial arts training.  Through training, experience, and proper instruction, we are able to use our imagination to create an imaginary opponent to fight against.  We are able to imagine being in the ring fighting against an adversarial opponent, or on the street against multiple attackers.
Advantages to Shadowboxing
Shadowboxing has many advantages to help you become a better fighter.  It can help you develop and improve technique, create combinations including kicks not suitable for the heavy bag, and improve your footwork and angles.  Shadowboxing can also help you improve your speed and explosiveness.  You do not need to purchase any equipment for shadowboxing (though I would recommend you do).  Finally, shadowboxing is a great cardiovascular workout.
Disadvantages to Shadowboxing
Like everything, there are disadvantages to shadowboxing.  You will not develop powerful strikes that you would on a heavy bag or focus mitts.  Resistance is important to strengthen your muscles and improve your striking ability.
You can only gain so much with fighting an imaginary opponent.  In order to make sure you combinations and strikes are fast and effective enough, you need to fight against a real opponent.  That way you can find out what does work and what does not when it matters most.
This goes along with knowing your strengths and weaknesses.  You do not know what they are unless someone with experience, or if you gain the experience by getting in the ring.
Conclusion
Shadowboxing is a very great way to mix up your training, but you should not assume shadowboxing is all you need.  You should incorporate shadowboxing into your workout routine, because it can only make you a better fighter.  It is another way you can avoid falling into a plateau and prevent from getting bored.