No idea what the Harry Potter game is, so I'll explain labyrinth so you can compare :)
You get a fold-out board with a few fixed map pieces.
You then have lots of other pieces with various markings on them, that get randomly placed all over the board, until it is all covered. You end up with a board covered in a maze.
You each (max 4 players, min 2) take three cards. These match pictures in the board, and are the things you attempt to "collect" during the game.
My kids are 7 & 5, so we play simply - you can get any piece in any order, whichever is easiest. We also don't hide pieces from each other, but I can see that this would make it a more interesting game.
When it is your turn, you take the spare map piece and push it into the board - this shifts the whole maze layout, so potentially ruins your plans of where you were going to move next.
The first person to get all of heir pieces is the winner.
I love playing it, and can see that it will be even more interesting as the kids get older. But even now, it is good :)