Bill,
Hook kick - general:
This kick seems to have been covered well by others, I would reiterate it can be a powerful and knock out kick. You can choose to use the sole of the foot in point sparing (as a slap) or if in full contact - or if you were comfortable or had the option of using in SD/street, you would use the heel.
When I was in TKD this was used a lot as per the video technique, however, interestingly when I switched to karate and goju ryu, the hook kick was favoured by the sensei in my club in tournament fighting and for him to devastating effect.
Combos:
This can be a very deceptive kick - one of my favourite combos was to throw up a front kick snap kick to the side of the head (say right temple/side of jaw) then if blocked or evaded immediately throw up again with same motion, same front leg but turn it into the hook kick at last second and connect to left side of jaw with heel, that = knock out or rocks opponent like hell. Unlike the video or in my TKD days, in my goju ryu training we chamber the knee even higher and make the lead leg/knee come right up the middle/centre line of the opponent, which when you throw a couple of punches first is quite deceptive in itself and is often missed or can be misinterpreted as an out of rage knee or what is to be turned into a front/stomp kick. When competing I have had a reasonable high success rate when using the above combo. I still laugh a bit about one of my first karate fights when I pulled this off (more than ten years back now); it was point/sport karate so I used the sole of the foot and effected a mighty slap to the side of opponents face; he did not go down of course but the look of surprise (we were ok buddies actually from the same club) on his face was priceless! : )
Also, as noted by Shihan smurf, this can be used beautifully when you move in for a punch and either the opponent moves back or you step slightly (only needs to be a slight step back for space if you chamber knee high) and then use the hook to the jaw. Depending on the competition rules and if you are allowed to maintain contact, ie hold legs/appendages of opponent or sweep, as also said below, I have used this effectively when grabbing the lead hand/arm of a punch thrown sloppily (or a block) or left out there too long and then come up and over the opponents held arm/wrist from the outside and connect to their head/face. I have only tried this with lighter/weaker/inexperienced opponents.
I know it's movie footage but check out Bruce Lee’s execution of the hook kick in say, Fists of Fury or Enter the Dragon to see the kind of speed and power that can be generated! There is also legitimate training footage of Lee practising this kick which is equally impressive. Anyway, it is not obviously going to have the same power behind it as a rear leg roundhouse but then that is not what the kick is about - the upside it is a much quicker/closer distance kick. Personally I generate most of the knock out power from the contraction of the hamstring in whipping the heel in the backwards arc into the target.
Again, as others have said, I have also used this to wind an opponent by striking the solar plexus with heel. Have also used this in a reverse spinning manner - but would only do this in training, I generally don’t like turning my back and opening up rear of leg (posterior cruciate ligament/hammies/calf) to leg attacks.
The one point I would say, is that while I have only been kicked in the groin by a counter once while executing this (a real shocker!), I do feel that if you are unlucky your groin is always open to a well timed counter/simultaneous kick from your opponent.
Usability:
Another point, sorry (!), is that I do not agree that this necessarily requires a lot of flexibility or is a “younger person’s” kick. My fight training sensei is late forties and the club/overall sensei who still kicks high is in his fifties (ok maybe that is still “young for some!....). If you focus more on chambering your knee high as can be and then extend the leg - for front kick - or hook the leg back, flexibility issues, particularly along groin regions, are reduce when coupled with regular dynamic stretching routines (rather than just static stretching). I have talked about this in length on some link ages back for Tez about high kicks and dynamic stretching exercise (I explain the exercises involved). These exercises allow the muscle groups the range of motion required and also the ability to “open” the pelvis (in a purely platonic context!!) to avoid strains/torn muscles. If you do these morning before work and preferably at night before bed on a regular basis you put your body in a position so that you can effectively execute high/head kicks “cold” (ie kicks to 95% execution without warm-up in street/unprepared situations). There was some old documentary about the Korean military or police who do this so that they can always do head kicks without fear of damage or need to limber up (the need for which kind of defeats the purpose of any martial kick!).
The other good thing with these stretching techniques is that when you are competing in knock-out or round-robin tournaments where you may need to fight three or four times on a night and may have issues otherwise staying “warm” between bouts; exercising the dynamic stretches in rest periods and just before entering the ring can overcome this problem.
I have used this hook kick once outside of tournament in a fight at a party when I was younger on a mate’s back deck. But unlike many, I have no issue using high kicks in SD or brawls if there is opportunity - pending environment/situation.