Those doors will open once the respective puzzle of that section is solved.
In the first screenshot, the section already has one open door. Behind it are either buttons to be found or blue objects to be clicked. Once solved, another door of the section will open, you solve behind there, another door opens, etc.
The second screenshot is a find the difference puzzle. You will notice that the objects on both sides of the door are placed almost identically. You find the differences (e.g. click an item on one side that doesn't exist in the same spot on the other side). When all differences are found, the door will open.