Terminology

MTC:  Missionary Training Center
There are 15 MTC's around the world.  Missionaries will first enter an MTC before going out to serve where they have been called. The Provo MTC (where Madeline is for the first two weeks of her mission) is a beautiful campus designed to accommodate up to 4,000 missionaries. The facility includes a large gymnasium, cafeterias, a medical clinic, a bookstore, a mail center, laundry facilities, classrooms, and residence halls. A day at the MTC can involve many different activities, including visiting the cafeteria, enjoying some exercise in the gym, and engaging in personal study. Missionaries spend much of their time in classroom activities.

http://www.mtc.byu.edu/themtc.htm
http://www.lds.org/locations/missionary-training-centers?lang=eng

District
In each mission missionaries are put in to districts which consists of four to sixteen elders. An missionary or elder supervises the district and he is called a district leader or DL. 

Greenie
A brand new missionary

Investigator
This is what missionaries call those who show interest in the Mormon church.

VC:  Visitor's Center
Part of Madeline's mission is to serve at the St. George Temple Visitor's Center.  It is built right on temple grounds next to the first temple built in Utah, the St. George, Utah temple. Inside you can learn more about the purpose of temples and the eternal nature of families.  Find a visitor's center near you by clicking here.

Zone 
Two to eight districts comprise a zone and includes 2 to 6 districts which has about 35 to 80 elders. The size of a zone varies according to the size of the mission and the preference of the mission president.
The persons who supervises the district leaders are called a zone leaders or ZL. 

http://mormonmission.blogspot.com/2008/10/lds-missionary-lingo.html