The importance of nature in this excellent tragedy lies in the way that nature reflects the heinous crime that has been committed by a series of natural events that show how nature has become disordered and topsy-turvy. If you are interested, this is precisely the same technique that is used in Julius Caesar to indicate how profoundly the assassination of a leader impacts not just the human world, but the natural world as well. Consider Act II scene 4 and the series of natural phenomena that are listed in the conversation that Rosse has with the Old Man. The Old Man says that:
Threescore and ten I can remember well;
Within the volume of which time I have seen
Hours dreadful, and things strange, but this sore night
Hath trifled former knowings.
They go on to discuss how a falcoln was killed by a "mousing owl" and how Duncan's horses became wild and actually ate each other. These events reflect and emphasise the profound disorder that has occurred in the human plane of existence. Let us remember that in Elizabethan times, the monarch was thought to be appointed by God, and therefore the crime of regicide was a very serious one indeed, which would have repurcussions that would reverberate not just in the human world, but in the natural world as well.