Source:  from http://www.revolutionbjj.com/ and http://bjjcanvas.com/

At this point of my BJJ career, competition plays an important part of my interest in our sport. It will probably change as I get older. I was looking at ways to explain this and found two great articles on the matter. Here the best parts from each:

“Many students of BJJ feel a burning desire go out and prove themselves on the competition mats.  This is all well and good for those guys, but for the rest of the community who see their teammates compete, or who are dimly aware that competition happens, competing might seem like a more risky endeavor than is worth doing.  The nerves that lead up to competition are overwhelming for many; the process of trying to diet or cut weight is daunting enough to discourage many more.

So… why should you compete in BJJ? 

Improves Your Ability to Maintain Calm in Adverse Situations
I consider this one of the most important benefits.  It can be attained in the gym by training hard and gaining confidence in your skills, but it is in competition where that calm is really put to the test.
So you have become confident in that environment because the psychological stress placed on you in training is very different from the stress you can feel in competition.
We all want to win when we compete, and it can be hard to be calm when things don’t go as planned. It is experience that helps you calmly assess the situation and move forward with the hand that you’re dealt.

Testing your skill level against people you don’t roll with every day 
Competing against people who don’t know your game is crucial to your developmental process.  If you compete well , this is the biggest difference from daily training at your gym.  So you can catch everyone at your gym with a guillotine choke.  What about the guy with superhuman strength and no neck from across town, or the guy who happens to have a great guillotine defense?
When I first started competing in Brazilian Jiu Jitsu, I was shocked at how well certain techniques I had previously (naively) considered unimportant actually worked.  Why?  Because all of my training partners knew very well the patterns of the fundamental attacks I was trying to use on them.  I had given the techniques a try, then discarded them from my daily rolling routine when my partners defended them.  Fortunately for me, I had still drilled them enough so that they were ingrained in me.  I found out that I was pretty good at the triangle choke, for example, by competing.

Helps Focus Your Attention on Weaknesses
Win or lose, you sometimes run into situations where you could have done things a little differently. In competition, there is an increased likelihood of that happening since you may compete against individuals who have different styles than you are used to in your gym.
It’s a great thing when it happens since it can focus you like a laser on areas that you can improve in. It can also serve as motivation for you to improve since you likely want to do better the next time you compete.
Improves Your Training by Giving You Short Term Goals to Focus On
When you compete, you want to win. If not, you wouldn’t invest the money and time required to do so.  Now given that fact, competition can focus your attention on the question of how you can improve in the shortest time frame possible.
Now any extra effort you’re putting into your training for a particular competition is speeding up your progress towards being a master of your art even if it’s only by an inch. It all adds up over time, and you become better than you would have been if you had never competed.

Invest in Your Art
When you invest, you can benefit even from losses because luck isn’t the primary determinant of the outcome.
So if you go into competition with the mindset that you are investing in your skills, you will benefit. There is no doubt of that.”

Read entire articles:
http://www.revolutionbjj.com/news/competing-in-bjj-or-grappling-why/
http://bjjcanvas.com/the-benefits-of-competition/