Not sure how far you are, but :
to the left the space is where you will have your birdhouse - you'll find bugs and picture pieces here.
to the right, the space is where your hammock will go when you build that - in the rest of that space you will have weeds and picture pieces.
 
Otherwise, it serves no purpose - it is just the graphic of the game.
 
Good luck!
 

As kids they study a lot.  Also, you can find them "playing cook", "playing office", and "playing in the workshop".  You can praise this behavior to encourage a career.  This is very helpful when you have an upgraded room and you want them to advance more quickly.
Just drop a child int the area of your choice and praise them when they are there.  Remember to make a note in their profile so you can more easily determine which child you had doing which task.
Good luck!