My own attempt to explain it in plain language has vanished into the ether, so here's another go. I couldn't understand this to begin with. Light dawned when I stopped thinking about chances of winning and thought about your chances of losing.

There are 2 goats and 1 car. With your first choice you're twice as likely to pick a goat as the car. Put another way, you're more likely to be wrong than right with your first choice.

The host then shows a goat and removes one of the possible wrong choices.

Remember, your first choice was more likely to be wrong than right and nothing's happened to change that - if it was probably wrong then it must be probably wrong now. Which in turn means that the only remaining door must be probably right. So switching will mean that you're more likely to win (but doesn't guarantee it)