Macbeth is delighted and can't wait to tell his wife, whom he refers to as his "dearest partner of greatness." He believes the prophecy will come true. He believes that he is destined to become king, and he needs to help make that come true. That would be his view of the world. We must take what is rightfully ours. His ambition is clear.
Lady Macbeth is going to provoke her husband to take what is his as well. She along with the witches will continue to egg him on. She has the same ambition for greatness--although at this point she goes beyond how Macbeth feels. Eventually, they will switch roles and the guilt will eat away at her.