Machines are tools that will give you cards in exchange for gems so that you can complete your Album. Each card will give you a prize if you place it on your Prize Board.
To access the machine room you will need to enter the game's Shop, select the gem icon at the top of the screen and tap on the "Get more cards" button.
When you enter, you will see three classic machines and the VIP machine. The latter includes cards from the temporary collections that you were unable to get at the time they were active.