The head positioning system is a voice-coil actuator. This is simply a coil of wire between two very strong magnets, identical in operation to a speaker's voice coil. Where a speaker is intended to faithfully reproduce acoustical movements up thousands of times per second, a hard drive's voice-coil accurately positions the heads anywhere within the defined range thousands of times per second.
It achieves ultra-high accuracy by continuously re-calibrating itself. This re-calibration eliminates drift from temperature changes, as temperature causes microscopic expansion and contraction of everything inside the drive, otherwise leading to alignment issues. Older drives which used stepper motors for the head position had difficulty adapting to temperature changes. So a modern drive is constantly readjusting itself for best performance.
The heads are "docked" or "parked" off the platter, using mechanical guides to lift them away from the platter. The heads are spring-loaded to exert some (small) amount of force towards the platter. Depending on the drive, it may spend most of its life in "parked" mode, where a kick wouldn't do it any harm.
When accessed again, they move out of the parked area, complete the operation, then park again. It may sense a misalignment and recalibrate immediately, or wait for the next scheduled recalibration, which happens in milliseconds with one tiny blink of the indicator LED (if it even reports this as "activity.") Some drives may use a "parked" area and an "idle" area, which is on the disk surface but not used for storage. That would obviously be faster so may be more common.
Even if a kick happened during a read-write cycle, the "cushion of air" is already pushing against the spring pre-load tension of the head, so a fairly strong kick is needed to cause a "head crash." That is where the head "dives" into the coating on the platter and physically scratches it off. That, for one tiny spot somewhere random on the disc would mean a slew of "bad blocks" congruent to the scratch length and width. Barring any other damage, such areas would be marked "bad" by a (long, "surface") disk format and the rest would work normally. But if this happened on track 0, master boot record, partition table, or other special areas, the disk could be totally unusable.
The voice-coil can be seen briefly in this video.
P.S. In the past, it used to be that the physical components of a hard disk were more advanced than the electronics. Thus, a hard drive failure was usually a physical defect, and data was only recoverable in a cleanroom environment by swapping out the failed component(s) with good ones. But today, the control electronics are far more advanced, and fail about as often (if not moreso) than the physical components. Er.go. if a spinning-platter hard disk doesn't work today, there is a 50/50 chance that replacing the controller board (which is fairly easy to do and doesn't require a cleanroom) will get it running again. Of course, a controller failure could have thrashed and abused the physical components, so any such working repair should immediately recover the data and assume the drive may die again at any time. And, cooling the disk also sometimes works, by microscopically shrinking everything inside. But this should be considered a destructive process, because room moisture condenses on cool objects and that's true inside the disk as well - get the data before it dies.