Democratic incumbent Roosevelt sought an unprecedented third term. Willkie represented the mainstream Republican Party. Landon, who'd gone down to defeat to Roosevelt in 1936, represented the isolationist wing of the Republicans.
The popular Roosevelt maintained much of the momentum that had already carried him to victory in two elections. While Willkie was popular among most Republicans, he simply did not distinguish himself sufficiently from Roosevelt on enough policies; he'd indicated that he would NOT dismantle the New Deal, and criticized Roosevelt's military build-up as being insufficient. Landon ran a generally lethargic campaign that syphoned more votes from Willkie than from Roosevelt.
The isolationists' concern that the U.S. might involve itself in the European war was also neutralized by the "big switch" of mid 1940, which saw Britain and France allying themselves with Germany against the Soviet Union after two years of fighting against Germany. Roosevelt took the additional step of cutting off all military aid to Britain and France in October 1940, just weeks before the election.
While the Republicans as a whole did better than they had in previous years, gaining seats in the Congress, Roosevelt's popularity, combined with Willkie's inability to distinguish himself and the votes lost to Landon, gave Roosevelt a comfortable victory that saw him with either a majority or a plurality in most states.
Ironically, while the US did avoid entering the European war, the United States was at war with Japan in January 1941, a mere two months after the election.
Democrat Franklin Roosevelt ran for an unprecedented third term, surviving a primary challenge from his Vice President, John Nance Garner. As in The War That Came Early, Republican Willkie struggled early on to distinguish himself, announcing that he would keep the New Deal, and concentrating instead on FDR's pursuit of a third term, before finally attacking FDR for plans to enter World War II. Roosevelt pledged not to send American troops into foreign wars, a pledge that came back to haunt him the following year. In the end, while Willkie did better than Roosevelt's two previous Republican opponents, it wasn't enough: Roosevelt became the first (and, due to current Constitutional law, presumably the last) US President elected to a third term.
Alf Landon did not participate as a candidate in 1940. Indeed, after his defeat in the election of 1936, Landon served the remainder of his term as Governor of Kansas, and never ran for public office again, contenting himself with working behind the scenes in the GOP.