The sidebar to the right under "New to the lore?" has a lot of the information on where to get started on lore.

Currently we are in year 31 ADP(After Dark Portal) and on Draenor in the alternate universe it is year -2 BDP(Before Dark Portal). BDP/ADP aka year 0 is the year in which the Orcish Horde led by Blackhand driven by corrupted demonic blood traveled from Draenor through the Dark Portal to the world of Azeroth and assaulted the human kingdom of Stormwind. After a bloody several year long war at which one point Blackhand was killed by his subordinate Orgrim Doomhammer who then took over leadership of the Horde, the Horde was victorious. The capital city of Stormwind was sacked and it's king Llane assasinated. The human survivors led by Sir Anduin Lothar then fled far to the north to the kingdom of Lordaeron and convinced it's king Terenas and the rulers of the other five human nations to form the Alliance of Lordaeron with Lothar as it's supreme commander.

After a second year long war in which the High Elves of Quel'thalas and the Dwarven clans of Bronzebeard and WIldhammer also joined with the Alliance, the Alliance was victorious and defeated the Horde at the decisive battle of Blackrock Spire in which Lothar was killed in single combat with Doomhamer. He was then defeated in single combat by Lothar's protege/second in command Turalyon and taken prisoner, resulting in the dismantling of the Horde.

That is just a brief summary of the lore and the history of Warcraft, and there's a whole lot more that happened before and after what I just typed out. Really I could and would go on all night like this, but the information in the sidebar would do a much better job of it.

If you do have any specific questions though, I will answer to the best of my ability.