Ashley Kannan has already given voice to the ideological distinctions between Lincoln and Douglas: Douglas being the champion of Popular Sovereignty and Lincoln a moral critic and opponent to slavery. In addition to this, I would like to speak a bit about the larger context in which these debates were held.
The United States of 1858 was in a state of crisis. After the Mexican War (along with the acquisition of Oregon from Great Britain), the United States grew substantially in territory in a very short time, and this created significant political instability within the country, as suddenly the precarious balance between slave states and free states was thrown in jeopardy by the long term implications of the territorial gains. Starting with California's application for statehood in 1849 (as a free state), the United States was beset by one controversy after another, as Abolitionists and pro-slavery advocates fought over the future of the territories and ultimately the future prospects of slavery as an institution. This growing conflict (that by this point had been escalating over the span of years) served as the backdrop to which the Lincoln-Douglas debates were held.
Politically it had significant implications. It launched Lincoln's reputation in the Republican Party, and was critical in getting him selected as its Presidential Candidate. On the other hand, Douglas's support of Popular Sovereignty actually hurt him among the southern states. Southerners wanted a blanket support for slavery, which Douglas's position could not guarantee. Thus, when the 1860 election was held, Lincoln comfortably carried the Northern States, the pro-slavery candidate Breckinridge carried the South, and Douglas was largely isolated between them. Despite carrying 29.5 percent of the vote (compared to Breckinridge's 18 percent and Lincoln's roughly 40 percent), he only received 12 electoral votes, against 72 for Breckinridge and 180 for Lincoln. In short, this debate seemed to have serious political implications in setting up the Civil War and the eventual end of slavery.