Henry had despaired for many years of having a healthy male heir with his wife, Katherine of Aragon. He blamed her for only giving him a daughter, as it was thought during Tudor times that the mother determines the gender of the baby, although we now know that in fact it is the father who does so. Additionally, and perhaps crucially, Henry had fallen in love with one of his wife's ladies-in-waiting, Anne Boleyn. He thought perhaps that Anne would be able to give him the son he wanted so badly.
Anne was a young aristocrat. She had been educated at the French court and was known as being quick-witted and highly strung. She was black-haired and dark-eyed and, although not as pretty as some, she was captivating.
I believe that she inspired the poem Whoso List To Hunt, I Know Where Is An Hind by Thomas Wyatt:
Whoso list to hunt, I know where is an hind,
But as for me, hélas, I may no more.
The vain travail hath wearied me so sore,
I am of them that farthest cometh behind.
Yet may I by no means my wearied mind
Draw from the deer, but as she fleeth afore
Fainting I follow. I leave off therefore,
Sithens in a net I seek to hold the wind.
Who list her hunt, I put him out of doubt,
As well as I may spend his time in vain.
And graven with diamonds in letters plain
There is written, her fair neck round about:
Noli me tangere, for Caesar's I am,
And wild for to hold, though I seem tame.
Henry put Katherine aside to leave the way clear to marry Anne. When the Pope (the leader of the Roman Catholic church) wouldn't agree to the divorce Henry wanted, Henry broke with the Roman Catholic church and set up the Church of England, making himself its head. The Church of England was Protestant, in line with the Reformation sparked by Martin Luther. Thus Henry brought the Reformation to England. Henry couldn't have Katherine murdered on trumped-up charges (as he was to do with later wives), because she was of the Spanish royal family and they were one of the superpowers of the time. In fact, the Spanish were to come close to invading and annexing England entirely in Henry's daughter's time.
So, long story short, Henry divorced Katherine and married Anne. She was to have several pregnancies but only one produced a living child, a daughter. The fact that Anne apparently couldn't give Henry the son he wanted led him to fall out of love with her. He said that she had bewitched him. He began to plot to be rid of her, as he had rid himself of Katherine previously.
Henry had Anne arrested and executed on patently false charges of adultery and treason. He even accused Anne and her brother George of committing incest.
Anne went to her death bravely, not knowing that her daughter would later become the most famous queen, in fact the most famous monarch in English history. Elizabeth I's reign was to far surpass Henry VIII's rule and is still remembered as a Golden Age to this day.
Read more about Anne Boleyn, or read about the third wife, Jane Seymour.