What two enemies does the kingdom of Scotland face? How are they overcome?

At the start of the play, the kingdom of Scotland faces two enemies: Norway and a rebellion led by the Scottish traitor to the throne, Macdonwald. Both enemies are essentially overcome on the battlefield. First, Macbeth and Banquo fight the rebels, led by Macdonwald. The injured captain tells Duncan that

brave Macbeth (for well he deserves that name)
Disdaining Fortune, with his brandished steel [...]
carved out his passage
Till he faced the slave [and]
unseamed him from the nave to th' chops" (Act I, Scene 2, lines 18-24).

He paints a vivid mental picture of Macbeth, slashing through a thicket of bodies to forge a path to Macdonwald, and, once he reached the leader, Macbeth thrust his sword through the man's stomach and ripped him open all the way up to his jaw.
Then, the captain explains, just as Macbeth and Banquo were turning away from their victory over the rebels, the Norwegian king saw his opportunity to attack while they were tired. The king then brought a fresh army, and even though Macbeth and Banquo were clearly alarmed by the prospect of another battle, "they doubly redoubled strokes upon the foe" and won (Act I, Scene 2, line 42). Scotland, then, really owes its safety to the bravery of its champions on the battlefield.