PaulK's explanation is correct, and here is a more intuitive example to help out in the intuition department...
Instead of three doors, there's a million doors. You choose a door. Pretty damn unlikely you'll win, right?
Monty eliminates only doors with goats, and eliminates 999,998 doors. Now you're down to your door, and one other. You can stick with your door, or switch.
Which would you do? Switch in a heartbeat, right?
So it is with the three door version, just not so obviously.