" I have no spur to prick the sides of my intent, but only vaulting ambition, which overleaps itself and falls on the other"
refers to his ambition as like a horse that he needs to tame, but he lacks the spur that would make him act on this "vaulting ambition"
he's aware that if he gives in to this ambition that it would lead to his "fall"-biblical language (the fall if Adam and Eve)- reminding the audience that this is going against God.
he wants it but he does not know how to go about it because of his moral conscience that tames his ambition.
which is further fuelled by Lady Macbeth's lingering emasculation