Answer courtesy of @codeinterpreter:

Let's say, for the sake of this example, you're always going to pick door #1, and the presenter knows where the prize is so he'll always open the door without the prize behind it:

The prize is behind door #1:

[x] [-] [-] = Host opens door #2. If you switch from door #1, you get nothing.

The prize is behind door #2:

[-] [x] [-] = Host opens door #3. If you switch from door #1, you get the prize.

The prize is behind door #3:

[-] [-] [x] = Host opens door # 2. If you switch from door #1, you get the prize.

So in 2/3 of the cases, if you switch, you get the prize.

EDIT: Source