The civil war that marks the beginning of The Tragedy of Macbeth is defined by rebellion and traitorous behavior against King Duncan. These events played out on the stage parallel the real-life rebellion and attempt on King James's life in 1605.

King James I of England was the reigning monarch at the time at which Shakespeare wrote Macbeth. The Gunpowder Plot was engineered by angry Catholics who decided to rebel against the Protestant King James and try to assassinate him. The plot did not succeed, but the treasonous behavior was enough to make the king extremely wary of his Catholic enemies from then on.

Many scholars believe that Shakespeare deliberately wrote in the civil war in Macbeth in order to reassure King James that the bad guys will always lose, and better yet, they will always be severely punished by the good guys. The rebels at the start of the play, Macdonwald and Cawdor, are indeed killed for their attempt to take down the rightful monarch, and the same happens to Macbeth at the end of the play.

In Shakespeare's Macbeth, there are really two civil wars:  the play begins and ends with civil wars.

At the start of the play, Macdonwald and Cawdor, two Scottish thanes, are revolting against the ruling monarch, King Duncan.  The two traitors are joined by an opportunistic monarch from another country, but he doesn't get much attention in the dialogue.  Macbeth, Banquo, and Macduff, presumably,  lead Duncan's forces in battle and defeat the traitors.  Macbeth, especially, gains favor and fame and reputation for his prowess on the battlefield.

By the end of the play, Malcolm, Duncan's son, and Macduff, lead an army against Macbeth that consists of both Scottish and English forces.  This battle, however, is very much over before it begins, since Macbeth's forces, for the most part, are no longer loyal to Macbeth.  Macduff defeats Macbeth in one-on-one battle, and Malcolm's forces are victorious. 

That the play's structure is encircled in wars is telling.  This is a violent and bloody drama--from the description in Act 1 of Macbeth cutting Macdonwald from the navel to the jaw (in other words, he disemboweled him), to Macduff entering the stage carrying Macbeth's head in Act 5--violence and blood and the unnatural dominate this play.