What is the story of the famous tragedy play by William Shakespeare named Macbeth?

The plot concerns the rise to power (and the subsequent
demise) of a noble warrior (he's called a Thane, which is like a Lord) of ancient
Scotland, Macbeth.  He begins the play fighting a battle in the service of the current
king, Duncan.  Duncan has decided to silence once and for all by two rebellious Thanes. 
When Macbeth proves himself loyal and courageous in battle, Duncan decides to add more
glory to him by bestowing one of the titles that had formerly belonged to the slain
rebel upon Macbeth.

Meanwhile, Macbeth and his comrade,
Banquo have been waylaid by three mysterious witches, who prophesy that Macbeth will
become Thane of Cawdor (the title that the king has decided to give him) and then King. 
They also say that Banqo will beget kings.  Macbeth and Banquo do not know what to make
of these predictions, but Macbeth is later surprised to note that the first prediction
has come true when Duncan makes him Thane of Cawdor.

Upon
returning home to his wife, Macbeth makes the choice that changes the course of the play
for him.  He decides to take his wife's counsel and murder Duncan so that he might
fulfill the witches' prophesy and become King.  He does the deed and does become King,
but this only, ironically, deepens his troubles.

He finds
he must murder Banquo and his son to prevent Banquo's children from becoming kings.  He
succeeds with killing his friend, but Banquo's son escapes.  He then must face other
prophesies from the witches and, ultimately, an uprising against him led by Duncan's son
and other Scottish Thanes.

The culmination of the story
shows Macbeth's decline into a desparate killing machine, and ultimately ends in his
death at the hands of those more honorable characters that would rule in his place.  His
wife, Lady Macbeth, is also overcome with her own guilt and goes mad and kills
herself.

The play is considered a classical tragedy.
Macbeth is a tragic hero whose tragic flaw is his own ambition.  In the beginning, it
seems to be the thing that raises him up, but ultimately, it is the instrument of his
own demise.

You can find more detail about the play in the
links to the Entoes study guide given below.