What is the definition of load factor and how do you apply it? I'm a little confused about the definition of the load factor, n, as the definitions I found seem to contradict its application in force and moment balance analysis of an aircraft structure.

The definition given in my university script states that the load factor equals the ratio of all external forces acting on an aircraft minus its weight, to the magnitude of the aircraft's weight; this implies that the load factor is the ratio of all aerodynamic forces acting on an aircraft to the magnitude of its weight.

The Wikipedia definition of the load factor states that the load factor is the ratio of the sum total of all aerodynamic forces acting on an aircraft to its weight. 

My script definition therefore tallies with the Wikipedia definition. All good so far. 

Now, however, there is also a sentence in my script that states that the load factor is a means of including all inertial loads and gravity loads in observing the loading of an aircraft; this implies that weight is included in observing the loading of an aircraft: this makes better sense to me, since, when expressing the loading of an aircraft, it would be easier to say that the aircraft is now being loaded "this many times its weight", compared to this many newtons; this however, contradicts the definitions above.  

And now to the force and moment balance analysis issue, I noticed that all components of an aircraft are expressed in terms of its load factor, which is fine, but then in performing the balance, the weight of the components are not considered. How can you ignore the weight force which is always acting on the aircraft when the load factor (per definition) excludes it? An added confusion is in that lift is considered in the moment balance, with all component's loading expressed in terms of load factor; how can you include lift, when it is already incorporated into the load factor of the components; this implies that the part is further loaded above its current loading. 

I would appreciate if someone can straighten up what the load factor means, and how should it be applied in force and moment balance calculations.
The load factor is the total acceleration you feel, pointing downwards. In straight and level flight, the load factor is 1: you only feel the acceleration of gravity. So a load factor 1 equates to 9.81 m/s$^2$ (If gravity was higher, let's say 15 m/s$^2$. load factor 1 would equate to 15 m/s$^2$. But that's another story.)

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Bank the aircraft 60° and fly a co-ordinated turn, and you'll experience a downward acceleration of 2g. This is a case that is easy to understand since it is a static situation with constant velocities. If we have a dynamic sine wave for instance, the load factor would be a function of where we are in the cycle, if the aircraft is accelerating up or down. The actual acceleration is added to the gravity vector.

Load factor does not ignore the weight of the aircraft: 


In steady horizontal flight, load factor is 1 because it is the same weight that would show up on a scale on the surface of the earth. 
All dynamic accelerations are added to 1. If the aircraft accelerates downward with -1g, the load factor is zero and everyone on board is weightless.
Forces are vector entities. For the load vector, we're only counting the resulting accelerations in the z-axis of the aircraft. After summing the forces in 3 degrees of freedom, the z-axis force F drives the airplane up/downwards with an acceleration of a = F/m.