The weight of an aircraft (including unmanned aircraft), and the manner in which the weight is distributed, will greatly impact the flight characteristics of the aircraft.
The center of gravity (CG) of an aircraft is the point on the aircraft where all of the weight is in equilibrium. If you found the perfect point on the aircraft where if you rested it on your finger (ignoring how heavy it was), the entire aircraft would balance, that would be the "center of gravity."
Always be sure to check the manufacturer's recommended CG limits for the specific UAV you are flying, and be sure to stay within those limits. These CG limits are often included in the aircraft operations manual, are posted online, or may be found by calling the manufacturer.
A definition that the FAA wants you to be familiar with is stability, which is the aircraft's ability to recover from a maneuver and come back to straight and level flight.
If the CG is to far to the rear on a fixed-wing UAV, the unmanned aircraft will have a very difficult time recovering from a stall, since the UAV may not be able to pitch forward and correct the critical angle of attack (remember from our Stalls lesson).
Two other terms that the FAA wants you to be familiar with are maneuverability and controllability.
Maneuverability is the aircrafts ability to withstand the forces exerted on the aircraft during flight, such as turns, climbs, and other maneuvers.
Controllability is how well the aircraft responds to inputs from the pilot.