In a talk by Elder L. Tom Perry he quotes:
"'Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs.' (John 21:15.)
Then the question a second and third time. And finally, Peter, being grieved, replied to the Lord, 'Thou knowest all things; thou knowest that I love thee. Jesus saith unto him, Feed my sheep.' (John 21:17.)
Finally Peter understood: 'when thou art converted'—a condition carries with it a responsibility to do something with that conversion, to feed the sheep of the Savior. The real value of our commitment through our conversion is when it is interpreted into action, when something results from that which has occurred from knowing the Lord."
Missionary work is a outward expression of a individual's love for God, and their love for their fellow man. I want to show my love for my Lord and Savior, and so I serve as a missionary.