A bough is a tree branch. A bow (which sounds like bough) is when someone bends forward at the waist as a way of saying thank you to someone or to show respect to someone. In theatre, after a performance is done, the cast will come on stage at the end and take a bow. The joke is personifying a forest and using the term "boughs" which is often seen on trees to mean "bows". 
The cast , after the scene in the forest , took their boughs .