The Machines are tools that give you cards to complete your card collection in exchange for gems. Moreover, each card has a prize that you will receive when selecting that card on your board.
To enter the Machine Room, you will need to tap on 'Get more cards', on the main board of the game called Album. Once inside the room, you will see three classic machines, a temporary machine (depending if it’s available at the time) and the VIP machine (which includes cards from the temporary collections that you couldn't get when they were available).