The convention met in New York City at the second incarnation of Madison Square Garden.
The front-runners were William G. McAdoo and Alfred E. Smith. McAdoo had been Secretary of the Treasury during most of Woodrow Wilson's presidency. He later represented California in the U.S. Senate for one term, from 1933 to 1938. Smith was governor of New York; after failing to win the 1924 nomination, he was nominated for president by the Democrats in 1928, when he lost to Herbert Hoover. Smith was the first Roman Catholic to be nominated for president by a major party.
The convention eventually compromised on Davis. He had been a congressman, solicitor general, and ambassador to the Court of St. James's (i.e., ambassador to the United Kingdom).
Davis lost the general election in a landslide to the Republican incumbent Calvin Coolidge, who had become president the previous year when Warren Harding, whose vice president Coolidge had been, died. Sen. Robert LaFollette of Wisconsin ran a third-party candidacy as the Progressive candidate, winning only the 13 electoral votes of his home state, but getting a significant 16.61% share of the popular vote.
Here is a link to an article explaining the disagreements in the Democratic Party in 1924 that led to the long convention deadlock, and landslide defeat in November. That party's divisions over racial issues, which did not result in a full-blown party split until 24 years later, were a major factor.
That article makes a plausible case that LaFollette's Progressive candidacy drew votes away from the Democratic ticket, thereby contributing toward Coolidge's landslide. The dynamics were different than in 1912, when the third-party candidacy of another Progressive Republican, Theodore Roosevelt, was widely seen as siphoning off Republican votes, and allowing the victory of Democrat Woodrow Wilson.