A tragic hero is traditionally defined as someone who has a flaw and it is this flaw that causes the tragic end of the character.
Macbeth fits this definition because at the beginning of the play, Shakespeare portrays an honorable man who fights for his king and country by slaying Macdonwald. He is eager to end the battle, and he is very honored to be rewarded with the title of Thane of Cawdor.
However, even in this first kill, that happens off stage, we see in him a violent side. He doesn't just kill Macdonwald. It is told through the captain that he slices the rebel from the knave to the neck, chops off the head and then fixes the head to a battlement. Even though he is doing it in battle, this first kill is violent, extraordinarily unnecessary.
It is the violence and corruption of his power that leads to his downfall in the end. Killing Duncan is not enough for Macbeth, he continues on a violent, corrupted spree by killing his good friend Banquo and then Macduff's entire family (without real purpose). His flaw continues to grow throughout the play and that, in the end, is what causes his own death - his propensity toward violence.