The processing of a fire mission involves three essential messages. These are the fire order, message to observer, and fire commands. These messages contain the necessary information to tactically engage the target, control the mission, and transmit technical fire direction to the howitzers.
U.S. Army Field Manual FM 6-40, Tactics, Techniques, and Procedures for Field Artillery Manual Cannon Gunnery (Ch. 5 intro)
A fire mission is a tasking order that involves military units specializing in cannon gunnery. That is to say, it's an operation carried out by the artillery as they carry out the job of providing fires. There are several ways that an artillery unit will provide fires. The first is a pre-planned fire. In this case, a pre-set sequence of targets and taskings have been assigned to the unit, and the unit (usually a battery) will service their targets in order at the times and with the effects specified in advance. The second is as a result of a call for fire, usually from a forward observer attached to combat forces. These trained personnel can contact the battery or a larger artillery unit and request fires against targets of opportunity- or they can provide timing for pre-planned fires. In the latter case, they might wait until the enemy has reached a pre-registered position and then send merely the third part of the fire mission - the fire command. A third case involves self-defense fires, in which case the fire mission will be generated by the battery or larger unit itself (although if an artillery unit needs to fire self-defense, things have gotten hairy indeed. If you hear 'LOAD BEEHIVE!' it's time to start thinking about making yourself scarce, unless you're manning the guns).
That was fairly long winded. Let's try to reduce it. A fire mission, therefore, is an artillery task that results in a single type of fire against a single target at a specific time. If your tasking involves multiple types of fire, multiple targets, or multiple times, then you will need more than one fire mission.