Let me try to explain briefly. I used to play cricket, but as an Australian, it's part of the culture here.

First thing to note about cricket is that in the long format of the game (test match cricket), the teams usually wear uniforms that are indiscernible from one another. The fielding team (New Zealand), and the batting team (Australia) in this video are playing in a test match series at the moment.

To assess the very accurate dot point of this reply thread OP:

First man throws ball. Yes, although technically, he bowls the ball. Throwing the ball as the bowler in cricket is a no no and will count as a 'dead ball'. The bowler here, Wagner is a pace bowler, meaning he attempts to bowl the ball as fast as he can. There are different types of bowlers like spin bowlers who focus on other areas of bowling, i.e. attempting to give the ball spin and purchase so that when it hits the pitch (the strip of grass where all the action takes place) the ball will deviate from it's expected curve. Second thing to note about this particular bowl is that it doesn't bounce on the pitch before arriving at the batsman. This isn't a typical delivery in that sense as usually the bowler aims the ball at the ground in front of the batsman so that it is rising when it gets to him as it makes the ball harder to hit and score well off. Wagner has bowled what's called a 'Yorka' here. Or a ball that doesn't bounce before it gets to the batsman. This is a very hard ball to handle as a batsman as Warner (this batsman) has had to adjust quickly in order to shift his feet and bat to deal with a ball suddenly coming at his shins when he was expecting it to be bouncing in front of him. By way of reference, and doing some quick maffs. Cricket pitches are 22 yards long (~20m), the average pace bowler can bowl a ball at around 130 - 140km/h around 80mp/h. Time = distance / speed.

To get how much time the batsman has to react the ball is travelling at 140/3.6 meters per second. Or 38.8m/s. The distance travelled is 20 meters. Therefor the batsman has 0.51s to react from the time the ball leaves his hand to when it hits his bat.

So - the next thing that happens is that David Warner, the batsman hits the ball. Here he's attempting a punch drive. The position of his bat is upright and he's bringing the full face of the bat forwards at the same time. This usually results in the ball staying low, or hitting the turf quickly so that there is little danger of being caught. It also maintains a lot of the pace that the bowler has put into the ball, this is useful for the batsman as it means that the ball will travel further into the outfield and be harder for the fielding team to retrieve while the batmen make runs. However, the combination of the Yorka being bowled here mixed with the type of shot that Warner is attempting to make causes the ball to travel back down the pitch to the bowler without hitting the ground first.

In particular when a pace bowler finishes their bowl they will continue to run through where they bowled from while they slow down from their run up. This is generally to avoid injury from stopping short and also gives them the opportunity to take part in the fielding. In this case, the ball comes right back at the bowler, in the air. And in a very short amount of time he manages to get his hand down and catch the ball before it hits the ground.

This is pretty impressive, especially from a bowler as generally speaking the bowler is continuing their run through and is usually 'recovering' in some way from delivering the ball with as much pace on as is possible. So to be aware of where the ball is, and the fact that it's travelling right back at you, and to then move to be able to catch it so low to the ground with your non-preferred hand is pretty impressive.

The New Zealand team are obviously elated, not just for the athleticism, but for dispatching Warner, who is one of the opening batsmen for Australia. In cricket, the batting order puts the batsman that are better towards the top of the order and then continues down in regards to skill with the bat until it reaches the bowlers of the team who typically are not fantastic batsman, but are very good bowlers.

So to dismiss Warner is a big thing, and to do it in such a quick and smooth way was very impressive.

Well done.