First, can I recommend that you try http://turtle.sugarlabs.org instead of the version included with sugarizer.org.
Regarding actions and boxes:
The idea here is that you can make a stack of blocks that can be reused over and over again. So, for example, a stack of blocks to draw a square: repeat 4 forward 100 right 90 can be put inside an action block, named square, and then, whenever you want to draw a square, call "do square". In essence you are extending the block language -- a new block even appears on the palette for each action you define.
This is analogous to variables in programming. Put a value in a box and then refer to the box to get the value back. For example, in a box called length you can store the number 100 (store in box length 100). Then in your square program as per above, you could say: repeat 4 forward "box length" right 90. You'd end up with the same 100x100 square as before. But then you could change the value in the box to change the size of the square: put 50 in the box and the square will be 50x50. Put 200 in the box and the square will be 200x200.
A common thing to do is to increment the value in a box, e.g., store in box length (box length + 10) would result in the value in the box increasing by 10. Put that in a loop and you see your square grow.