Debates have always had winners. If the only purpose of debates were to describe the candidates' positions, they would just be campaign speeches. This is valuable, but it would be better served by a town hall style forum, where audience members ask questions directly. Debates give the candidates a chance to confront each other and demonstrate who is the more persuasive and who really has the best understanding of the situation. There's of course no formal winner in a political debate (unlike, for example, on a school debate team where a judge decides the winner). But pundits and voters can collectively decide which candidate was more persuasive and convinced more voters to support them.
Probably the most famous early public debates are the Lincoln-Douglas debates of 1858, which are the earliest mentioned here so far. In these debates, Abraham Lincoln and Stephen Douglas, who were then candidates for the Senate, debated primarily the question of slavery. While Douglas won the election, Lincoln's debate speeches were well received and widely republished (not as common then as now) and helped bring him the national prominence needed to win the Republican nomination in 1860.
While today we remember the 1980s as being dominated by the presidency of Ronald Reagan, the 1980 election was not a sure thing. Somewhat like today, the overall voting public had serious concerns about Reagan's age and his ability to withstand the stress of being President. Reagan already had a lead going in, but he had a good debate, convinced the country that he was up to the job, and never looked back.
Many well-remembered political moments happen during debates. "There you go again," "I feel your pain," "Whole binders full of women." The authentic, off-the-cuff remarks needed in a debate give viewers a more accurate understanding of the candidates than any number of advertising spots or prepared speeches. Like so much of politics, it's not really about the ideas, it's about the candidate, personally, as a leader.