In many Shakespeare plays, the climax occurs at the end of Act 3. Therefore you need a summary of Act 1, Act 2, and part of Act 3.
In Act 1, a group of witches are having fun. They have decide to give Macbeth three prophecies about his future: that he will be Thane of Cawdor, that he will be king, and that Baquo’s sons will be kings. At first Macbeth and Banquo laugh them off, until Macbeth is indeed promoted. Macbeth writes a letter telling his wife, but then Duncan names his son Malcolm next in line for the throne. Macbeth gets mad.
Stars, hide your fires;
Let not light see my black and deep desires:
The eye wink at the hand; yet let that be
Which the eye fears, when it is done, to see.(Act 1, Scene 4)
His wife is also mad. Fortunately, Duncan is coming to their house to celebrate. She hatches the perfect plan—they will kill Duncan, and frame the king’s two sons. That way, Macbeth will be next in line.
Macbeth does not want to at first, but she talks him into it. He follows her orders to the letter, and slays the king. Malcolm and the king’s other son, Donalbain, flee. Macbeth is named king.
Things do not go smoothly. Macbeth is not satisfied.
To be thus is nothing,
But to be safely thus. Our fears in Banquo
Stick deep, and in his royalty of nature
Reigns that which would be fear'd. (Act 3, Scene 1)
Macbeth hires murderers to kill Baquo and his son Fleance, to make sure the third prophecy does not come true. They succeed, but Macbeth has a vision of Banquo’s ghost and starts to wonder what he was really getting himself into. We are approaching the climax, or the most interesting point--the turning point.