Why do Mormons go on missions?

As a convert to the Church, I was not raised in a typical "Mormon" home. I didn't have the same push that most missionaries are given by their families in fact I received almost nothing but indifference to my going, except from my sister who is also a member who believed that I would benefit from leaving on a mission.
But I made my decision when I was converted in the second lesson the missionaries held with me when I was just 11 years old. I knew that the power of God was given to these two guys in suits, and I wanted to be just like them. I just never knew why.
While on my mission, I had a day that changed my life. I was serving in a little town in Kentucky, USA, and I had a strange request from a member who was crippled from a car accident. You see, his garbage can sat right next to the road, and people had been throwing trash in it for months since his accident, and there was rain water that had filled it almost completely full. It had sat this way for nearly 8 months. He asked my companion and I to clean it out for him, and in reality my companion couldn't even move the can to begin with, so it was basically on my shoulders. I said yes, and when I walked up the road to the can I thought to myself, "What in the world have I gotten myself into?" I could smell the can from 10 feet away, there were flies buzzing around it, red water within it, algae growing over it it was probably the most disgusting thing I've ever witnessed firsthand, and I had agreed to clean it. So, I did so, and while I won't go into all the little details, I'll say that this took nearly 2 hours to clean out a 40 gallon garbage can, with me working the entire time. It was by far and away the most difficult to stomach thing I've ever done in my life, and when I finished, this dear brother was sitting on his porch in a wheelchair. As I placed the can back where it belonged and finished putting away the supplies, I walked past the porch and muttered, "Brother E------, you're lucky I love you."
It was at that point I knew I had changed from someone who cared not for any other humans in anything more than a superficial way I had learned to love others in the most extraordinary way imaginable I loved how Christ loved. He would have compassion, determination, patience, strength, devotion, and a myriad of other ways of not only feeling but showing his love through charity, the pure love of Christ. It brought me to tears just seconds after saying such a simple phrase because I thought back to all the people my mission had taught me to love even more my family, my friends, my missionary companions, my mission president, the people whom I taught the gospel, the people who rejected the message which we were happy to share, the leaders of the Church, the members of the community around me, and all of the random people I had come across through the days I had spent in the service of the Lord.
I don't know why most Mormons go on missions. It may be out of obligation, curiosity, sincere desire to serve, devotion, because the Lord commands all worthy males to serve, to bring others to Christ, or a plethora of other random and inventive ways to convince ourselves for going. But I know that the reason the Lord wanted me personally to serve a mission was to learn to love as He loves, to see as He sees, to serve as He serves, to become closer to what He is.