Brief Summary
The Set-Up
The antebellum period included a series of events and legislation about slavery, especially the Kansas-Nebraska Act and the Dred Scott decision, which exacerbated existing tensions about the expansion of slavery into the west.
Abraham Lincoln was pretty annoyed with how the debate over slavery was going, so when he had a chance to get up and make a political speech, he did not mince words. No more Mr. Tall Nice Guy.
The Text
Lincoln introduces the "house divided" theme in the first section of his speech to illustrate just how bad the situation was in America. He flat-out says that, soon, the U.S. will either allow or ban slavery everywhere…meaning those anti-slavery Republicans in the audience may have to put up with slavery in their neighborhood.
To really drive home how real this threat is, Lincoln gives a detailed history of recent events in America that have illustrated the danger of an impending all-slavery America. The two main events are the Kansas-Nebraska Act of 1854 and the very recent Dred Scott decision of 1857. He's basically saying: "You think I'm exaggerating? Nope. Looks at the reasons why this is a very real thing you should worry about."
He also lays into his opponent for the senate seat, Stephen A. Douglas, whom he would soon face off with in the WWE of political debates, the Lincoln-Douglas debates. Lincoln goes into all the reasons why Douglas' idea of popular sovereignty won't stop slavery, and might be a conspiracy to spread slavery nationwide.
He wraps up with a confident assertion that Americans will definitely keep this rickety house from falling down, London-bridge style.
TL;DR
The U.S. is going to have to decide to allow slavery everywhere, or nowhere—and the way things have been going, there's a real chance it'll be slavery everywhere.