There wasn't a real official title for this speech—it was Lincoln's response to being nominated as a senatorial candidate. It's always been known as the "House Divided" speech, though, referencing the biblical quote he uses in the beginning to establish a metaphor for the chaos that was the United States at that point.

The most famous line in the speech starts off with a quote that isn't even Lincoln's. "A house divided against itself cannot stand" actually comes from the Book of Mark (3:25).

The danger of a divided house is a pretty perfect metaphor for Lincoln in this case. The purpose of the speech was to basically make the audience face the reality: that there was a real chance the Supreme Court would soon take away states' rights to ban slavery. The sectional division over the slavery issue had increased dramatically in the 1850s, and given that the Civil War broke out less than three years after this speech was given, clearly the situation was at a boiling point.

Lincoln extends the metaphor later, like when he talks about "a lot of framed timbers, different portions of which we know have been gotten out at different times and places and by different workmen" (72) in order to bring the country to where it was by that day.

Really, the beginning paragraph of the speech is what people generally know and remember, and that's why the speech is called the "House Divided" speech. They remember that, and, you know, the way he was proved 100% right.