In baseball, the hitter ("batter") gets three chances to hit the ball every time they are 'batting' (waiting for a ball to be thrown to them). Each time they are 'at bat', they are given three chances to hit the ball. When they miss the ball, it's called a 'strike'. When a batter gets three strikes, they have 'struck out' and have failed to hit the ball. "he struck out three times" means he had 3 chances 'at bat', with three tries to hit the ball each time, and he missed every time. (the batter failed to hit the ball 9 times.)