Through means going in or starting at one side and coming out or stopping at the other side of: a path through the woods.
Throughout means in every part of (a place or object)
There is a good deal of overlap,and either would be appropriate in most circumstances. Through often has a sense of one end to the other, while throughout suggests into every corner.
The latter give a slight feeling of being more pervasive than the former. "He sent his scribe thoughout the land."