What exactly is the neurobiological mechanism behind the functioning of the human muscle?
Both recruitment and firing rate contribute to the overall "strength" of muscle action, but there are early and late stage depending on the load under which the muscles are operating.  This allows more precision for lighter objects (where muscle recruitment is the dominant mechanism).  For heavier objects, most of the muscles get recruited and all the body can do at that point is increase the firing rate more.  Note that throughout the whole process, both mechanisms are occuring: it's just a matter of which mechanism dominates at which stage/degree of muscle exertion.

And this makes sense: for smaller objects that you will be manipulating, you want more precision, so having muscle recruitment control gives you that spatial precision that allows you to manipulate objects (like tools) in novel ways.  Whereas when you're just trying to lift  a giant rock, to block a small stream, there isn't much precision required, you're just trying to get it to go a general direction (up and over), so you recruit all muslces and drive the spiking frequency as high as it will go.  Whether you fail or not at these extreme loads depends on your personal pain tolerance and your muscle's tensile strength (people with a higher pain tolerance are more likely to snap a tendon or muscle, or even bone).