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. Brad spent his first two weeks of his mission at the South Africa MTC. 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.

https://www.lds.org/locations/missionary-training-centers/south-africa?lang=eng
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. A 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. 

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. 

Transfer
Missionaries referred to being assigned or moved to another area as a transfer. 

P-Day
Usually on Mondays missionaries have what they refer to as preparation day or p-day. From the time they wake up until 5 p.m they are suppose to clean their apartments, wash their cars or clean their bikes, go grocery shopping, write or email their families, and engage in recreational activities that are not contact sports that give them some exercise.

Exchanges/Splits/Divisions
In order to maximize missionary efforts sometimes missionaries go out with members in a ward which is called a missionary exchange. When two missionaries go out with two other missionaries for a night or day or two it is referred to as divisions or splits. It is usually done with district leaders to train senior companions or with zone leaders to train district leaders. Sometimes it just gives missionaries a break from their companions.

White Washed
When two elders open a new area it is called white washed. There are several variations that happen depending on what the mission president feels is best for his mission.

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