A batter has two numbers: balls and strikes. When the batter gets 3 strikes, they're out. If they get 4 balls (pitches that aren't in the strike zone), they walk (advance towards first base).
If a batter swings and misses at a pitch that would normally be a ball, it's considered a strike. If he hadn't swung, it would have been considered a ball.
The point of the video is that at the professional level, batters should be able to tell quickly when a pitch will be as 'off' as the one in the video - so why wasn't the batter able to?