Buckingham Palace is the official London residence of her Majesty Queen Elizabeth II. You are able to tell when she is in residence by her personal standard on the flagpole which flies when she is home.
Originally this building was the London home of the Duke of Buckingham, hence the name, but it was bought by King George III and Queen Charlotte in 1762. It has been renovated several times over the past centuries with the East Front being built in 1847. That's the area which you would most likely see, being the side which faces the Mall.
Several areas are open to the public including the Royal Mews which houses the state carriages. One such one being the gold state coach used for coronations.
You might want to see the Changing of the Guard which takes place from April to July at 11:30 and on alternate days from August to March.