Yes, here it means the distribution of passengers and baggage in the aircraft. If the center of gravity after loading is too far forward or aft, you can end up with an aircraft that can take off just fine but then become unflyable.
There's actually a fascinating video if a cargo plane crashing just after a take off due to large cargo not secured properly and moving and changing the center of gravity: https://www.youtube.com/watch?v=M01RmcKsm2k
To be a little more descriptive, it's a dashcam video from a vehicle driving near Bagram Airfield, and you see the plane crash in a way that makes it clear that the entire crew are killed.
Some more detail from the Wikipedia entry[0]:
"On 2 June 2013, investigators from the Ministry of Transport and Civil Aviation of Afghanistan confirmed the load shift hypothesis as the starting point: three armoured vehicles and two mine-sweeping vehicles, totalling 80 tons of weight, had not been properly secured. At least one armoured vehicle had come loose and rolled backwards against the airplane's rear bulkhead, damaging the bulkhead. This also crippled key hydraulic systems and damaged the horizontal stabilizer components - most notably the jackscrew, which rendered the airplane uncontrollable.[10] Control of the aircraft was therefore lost, with the abnormal pitch-up rotation, stall, and crash to the ground ensuing.[1] The damage made it impossible for the crew to regain control of the aircraft."
You measure up front and plan. Doing a weight and balance calculation is a standard (and critically important) part of flight planning. For light aircraft in particular it is _really_ important because there is very little margin for error. With light private aircraft you're weighing yourself, your passengers, your bags, and the fuel load and you're only taking off if you're within a safe envelope.
I'm not familiar with airline operations because I've never flown anything bigger than a Cessna 172, but from what I gather the airlines assume an average per-passenger weight, and account for number of bags and the ground crew will distribute in the holds accordingly. Ever seen flight crew moving passengers on little regional jets? It's to make the weight distribution safer. The smaller the plane, the bigger the effect of a few passengers.
