Can anyone define exactly what a "transient" means, and how (or if) this differs from the drum hit itself? Thank you folks.

Definition from Sweetwater is pretty good, "A non-repeating waveform, usually of much higher level than the surrounding sounds or average level. Good examples of transients include the attack of many percussion instruments, the “pluck” or attack part of a guitar note, consonants in human speech (i.e. “T”), and so on. Due to their higher-than-average level and fleeting nature, transients are difficult to record and reproduce, eating up precious headroom, and often resulting in overload distortion. Careful use of compression can help tame transients and raise average level, although over-compression will result in a dull, squashed, flat sound to the signal."

Think of when a stick hits the snare. It pushes the head of the snare inward, then the head snaps back rapidly. As that back-and-forth movement repeats, it causes air molecules to be compressed and rarefied into waves, which are what our ears interpret as sound.
But it makes sense that the waves that are created immediately after the hit will contain more energy. As time elapses, more and more energy from the hit will be lost due to frictional forces in the snare head, air resistance, gravity, etc. It's like if you pushed someone sitting on a swing set--they will travel the farthest distance after your push because the forces that will ultimately slow them down haven't had a chance to do that as much yet.
Transients are much higher in frequency than the other energy in a sound. That's because more energy is transferred immediately after the hit, so the oscillating material vibrates more rapidly. Since frequency is the number of times the material vibrates back and forth per second, we know that faster vibrations will equal higher frequency.
Instruments like snares and triangles dissipate their transferred energy very quickly. That's why they consist almost entirely of transients, which is easy to notice when observing the waveform. They are made of material which isn't designed to vibrate on its own for extended periods of time, unlike a guitar string.
Fingered basses, on the other hand, typically have weaker transients which are much closer in level to the average level or sustain of a held note. The transient is still there, it just isn't as noticeable because the fingertip isn't as efficient in transferring energy to the string, and because the RMS energy in the sustained note is much higher relative to the transient. Sometimes the transient is even too weak to be heard clearly, in which case you can use a compressor to exaggerate the bass note's transient so it can be distinguished more easily in the mix.
And that's the most powerful thing about compressors, really: they allow you to play with the transient/sustain balance to get the sound you are looking for. Shorter attack times grab the transient sooner and reduce it in level, while longer attack times let the transient push through before the compressor grabs the signal, which makes the transient punch through the mix more effectively.

Thank you guys, I get it now.