In simple terms, a half-volley is a strike of the ball that is made just as it is bouncing up off the turf, rather than whilst it is sitting still or floating through the air. The reason it can generate such power is all down to the timing, because catching the ball at exactly the right moment allows all of the energy from your swinging leg to transfer straight through it. Get it spot on and you can send the ball flying towards goal with a ferocity that is difficult to achieve any other way, whilst also keeping it low enough that a goalkeeper struggles to get down to it in time to save it.
It would be fair to say that this isn’t a skill attached to any one particular player, given the fact that it has been a part of the game for as long as people have been kicking a ball. That being said, some of the most memorable goals in football history have been half-volleys, with players such as Steven Gerrard and Alan Shearer becoming particularly renowned for producing unforgettable strikes using the technique. To pull it off, you need to watch the ball closely and get your body over the top of it, striking through the middle of the ball with your laces at the very instant it bounces.
The difficulty with the half-volley lies entirely in the timing, because the margin for error is desperately small. Connect with the ball a fraction too early or too late and the whole thing falls apart, either scuffing along the ground or sailing off into the stands. That is why this is a skill that rewards hours and hours of repetition, ideally getting a friend to throw or chip balls towards you so that you can practise meeting the ball cleanly on the bounce. Do that enough times and it will begin to feel natural, at which point you’ll be able to bring it out during a match.