It's the difference between the probability that a particular door conceals a car and the probability that you will make the correct choice. The first remains fixed (depending on the number of doors to choose from), the second depends on how much information you have.

Someone coming along at the second stage of the game where there are only 2 doors to choose between has no information on which to base his choice. He faces an entirely random choice between two doors. His chance of winning is therefore 50/50.

The original contestant is not making a random choice at the second stage, because he already has some information. From the situation which applied to the first round, he knows that there is a 2:1 chance that his first choice was wrong. By using this knowledge (which is not perfect, but better than none at all) he can therefore improve his chances of winning to 2:1 by switching.

Suppose someone had tipped him off which door the car was actually behind. With that knowledge his chance of winning increases to 100%. There's still only a 1 in 2 chance that a particular door hides a car.