Let me see if I can explain what "loading" means in this context. For those of you that work for a railroad and already understand this process, keep in mid this is a very simplified explanation. Let's not over-complicate things here.
The electrical power generated in a diesel-electric locomotive is controlled by a device called a "Load Regulator." The DC generator (or AC alternator) does not generate any current unless an excitation voltage is applied to the field coils of the generator/alternator. This is what the load regulator does, in response to the throttle position and speed of the locomotive. The excitation voltage is a low voltage, low current source, that controls the output of a high voltage high current generator or alternator.
When the throttle is advanced from idle to Run 1, the load regulator moves to apply a small excitation voltage to the field coils. The generator/alternator then produces a low voltage which is fed to the traction motors. The amount of voltage developed is directly related to the throttle position and the speed of the engine. As the throttle is advanced further, the Load Regulator increases the excitation voltage. The generator/alternator also produces a higher voltage, resulting in more current being fed to the traction motors. All the while, the Load Regulator is balancing the demand for power with the speed of the prime mover and the load demanded of it.
The current being drawn by the traction motors will show in the cab on the Load Meter. At 100 amps or so, the locomotive will just begin to move. When working all out in Run 8 at the minimum continuous speed for the locomotive, the current draw can be 1,000 amps or more.
When the throttle ultimately gets to Run 8, the Load Regulator will be adjusting the excitation voltage to the maximum it can be without over loading and slowing down the prime mover. Incidentally, no engineer is his right mind would EVER go from idle directly to Run 8. Not only is it against the rules, it is terrible train handling practice and will result in a lot of wheel slip or yanking the train in two. That's NOT how it is done. There are situations where Notch No. 2 pulls better than Notch No. 8.
When an engine is said to load quickly, it means that there is a very quick response between the throttle and increased amps on the load meter. In other words, when the throttle is moved, the engine quickly starts to move. Switchers are typically set to load faster than road engines. Thus they respond quickly to changes in throttle position, which is a big help when switching. When I say "quickly" I mean they respond within one or two seconds to a change in throttle position.
GE locomotives are notoriously slow to load when compared to EMD models. You can make a throttle change in a GE and it may be 10 seconds before you see any change in the load meter. And when the Load Regulator in a GE starts doing it's thing, it does it VERY slowly. The amps (and the pulling force) increase very slowly in a GE when the throttle is advanced. I think this is GE's way of making sure that their locomotives provide smooth train handling, regardless of how ham-fisted the engineer might be. Switching with a set of GE's is a nightmare because they are sooo sloooow to move when the throttle is opened.