Obviously, Macbeth is undone in the end by the political conflict he provokes with Macduff, Malcolm, and the other nobles who rise in opposition to him. But the most important, and certainly the most memorable conflict in the play is internal. While he is undoubtedly ruthlessly ambitious, Macbeth is also tormented by the moral implications of his actions.
The most famous manifestation of this is in Macbeth's soliloquy in Act I, Scene 7. Here Macbeth's conscience nearly overcomes his ambition. He says that Duncan is here [meaning Macbeth's castle] in "double trust" as Macbeth is both his "kinsman and his subject." Furthermore, Duncan has been a good king and a good man, and nothing but "vaulting ambition" could possibly drive Macbeth to murder him.
Shakespeare illuminates Macbeth's inner conflict later, in Act III, Scene 4, when the specter of the recently-murdered Banquo appears at the banquet table. Macbeth entreats the ghost not to "shake thy gory locks at me." Later in conversation with his wife he says that he is:
Stepp'd in so far that, should I wade no more,
Returning were as tedious as go o'er.
By the end of the play, the internal conflict is essentially gone, as Macbeth, having been responsible for so many deaths, now views death and murder with a sort of existential resignation:
I have supp'd full with horrors;
Direness, familiar to my slaughterous thoughts,
Cannot once start me.
But this is certainly not the case earlier in the play, when Macbeth's ambition and his conscience are in conflict.