There are two battles at the top of Macbeth. Whenever I am in charge of the staging, I try and open the show with both of these, just to make things clear. But whether or not they're staged, they are laid out in Act I scene ii. Appropriately, they come from two sources - the Bloody Sergeant, and the Thane of Rosse.
The first battle is the nearest, fought right on king Duncan's doorstep. We know this because his son Malcolm was in it, and almost captured. The Bloody Sergeant got wounded keeping Malcolm safe, and Malcolm has returned with the king, his father - or else, the Sergeant is being carried from the field. Either way, this is the first battle we hear about, from the Sergeant's own lips.
He tells us that the battle was looking bleak, and he names the reason why - "the merciless MacDonwald, worthy to be a rebel..." Note, MacDonwald is a Scottish lord, joined with the enemy (supplied with soldiers from the small islands nearby). Historically, this was common in Scotland. Norway had a strong foothold in Scotland, and many thanes swore oaths of loyalty to one or both kings, Norway and Scottish.
But history isn't necessary to the story. The facts as laid out tell us enough: MacDonwald has betrayed Scotland, and was winning the battle until Macbeth arrives. With Banquo fighting alongside him, Mac fights his way through the press of Norwayans until he faces MacDonwald. They fight, and Mac "unseems" the traitor "from the nave to the chops" (what a great turn of phrase). Then Mac fixes the traitor's head on the battlements.
But that battle isn't done. Seeing that Mac's forces are distracted, the Norwayan lord takes advantage and, reinforced with supplies and fresh men, attacks. But Macbeth and Banquo "doubly redoubled strokes upon the foe" and win the day.
That takes care of the first battle, close at hand. The second is taking place at the same time, in Fife. One supposes that King Sweno (Sven) of Norway planned a two-pronged invasion - one north, one south. And, arguably, the northern attack was the most dangerous, because "Norway himself" is there, leading his troops on. Here, too, there is a Scottish traitor - the Thane of Cawdor. And here, too, they are beaten back by a Scottish lord.
This is where productions go awry. 99% of the time, people play it as if it is Macbeth who has won the battle in Fife. Some productions go so far as to add his name to Rosse's speech relating the events. But it seems ludicrous to me. Given the immediacy of the current battle (the Sergeant is still bloody and his wounds have yet to be tended), and the distance to Fife, Macbeth would have to be in two places at the same time. Now, I grant that this is a story with elements of magic, but really, no, it isn't right. Besides, in Rosse's speech, the true hero of the battle in Fife is unnamed, referred to only as "Bellona's bridegroom."
But, wait - Fife? Fife is an important place in the play. Why? Because Macduff is the Thane of Fife.
Which means that it is Macduff who has captured Cawdor, turned back the Norwayan king, and won not only the battle but a huge sum of ransom from the enemy forces. This makes even more sense when you realize that Rosse and Macduff are cousins, just as Macbeth and Duncan are kinsmen. Rosse comes from Fife to bring Duncan the news of his cousin's great feat.
Which brings up an interesting point. Duncan gives Cawdor to Macbeth, his kinsman, not to Macduff, who earned it. Already there is strife between these thanes. Just as Macbeth feels he should be Prince of Cumberland, not that coward Malcolm who had to be protected and who fled the field to find his father, so too does Macduff feel he should be Cawdor, a title he earned with his sweat, toil, and blood.
This is why I get frustrated when I see productions where Macduff is hanging around with the king at the start. His arrival at Inverness is his real entrance, and he's arriving with hopes to be honored for his great travail. Awkwardly, he's coming to the castle of the man who has been given the title he himself feels he's earned. It allows for a whole world of play.
But all of that is beside the point I want to make here, which is simply that there are two battles, two traitors, and two heroes at the start of Macbeth.
Taken together, these two battles are immensely important. They symbolize the final expulsion of Norway from Scotland, thus creating, for the first time ever, a single unified Scottish nation - Alba, or Scotland.
Also note that it is Malcolm, at the end of the play, who brings the English forces into Scotland. It is also Malcolm who turns the thanes into earls, an English title. So, even setting aside the historical Macbeth (a great king who ruled for almost twenty years) - who is the true villain, in the eyes of Scotland? Macbeth, a bloody Scottish tyrant, or Malcolm, who set in motion the perpetual English claims on Scottish lands?
Food for thought.