mission: a person (missionary) chooses to dedicate all of their time to serving, teaching, and inviting others to come unto Christ for 18 to 24 months, leaving behind all other personal affairs; a mission also refers to a geographical area to which a missionary is assigned to serve for that period of time
companion: The Lord has taught us to go out and preach the gospel two by two (see Doctrine & Covenants 42:6), so each missionary has another missionary (called a companion) with him or her at all times.
Elder: a title used in the Church for males who have received the Melchizedek Priesthood. Male missionaries are referred to as "Elder," as well as most leaders in the Church.
mission president: a man called by inspiration to preside over the geographical mission; he and his wife are in charge of the missionaries serving within the mission
area: a smaller geographic unit within the mission where missionary companionships are assigned to serve for six weeks or more
district or zone leader: an assignment given to an Elder serving in the mission to supervise smaller groups of companionships; there are several district leaders under each zone leader
*there are also leadership positions for sister missionaries, called sister training leaders
P-day: officially known as "preparation day," one day each week where missionaries are able to do laundry, email home, purchase groceries, and other necessary errands, as well as participate in recreational activities as approved by the mission president
investigator: a person currently being taught by the missionaries
ward: a local congregation organized geographically, members attend the ward near their home
[click on the words to be directed to the lds.org or mormon.org page where the definition is given]