The only real impact of the debates between Abraham Lincoln and Stephen Douglas in 1858 was that they put Lincoln on the national "map" as a major political figure.
The debates were staged as part of a race between the two men for a seat in the US Senate. Douglas won the election. Even so, the debates catapulted Lincoln into the public eye. They were widely covered by various newspapers because Douglas was such an important national figure. Debating Douglas allowed Lincoln to become much better known and therefore contributed greatly to his becoming president two years later.
The Lincoln-Douglas debates were a series of debates during the 1858 US Senate elections between republican candidate Abraham Lincoln and democratic candidate Stephen A. Douglas. The impact of the debate dealt with slavery and states rights issues.
Douglas argued in the idea of popular sovereignty, where states should be given the right to decide by popular vote whether or not they would adopt slavery upon admission as a state to the US. Lincoln argued that slavery was morally wrong, noting that Douglas was using the argument of popular sovereignty to extend slavery into the western states. The debate brought up moral issues, potential violations of the Declaration of Independence, and slavery vs. popular sovereignty.
To echo the sentiment of the previous answer, the Lincoln-Douglas debates also catapulted Lincoln into the public eye, with the later effect of making him a promising presidential candidate. Prior to the debates, Lincoln was a relatively unknown politician.