The underdog archetype is generally a character that has some natural talent in an area, but is also lacking in other areas. Perhaps the underdog is lacking in experience or proper gear. The underdog is always predicted to lose, but usually wins. In some cases the character does in fact lose the competition but wins in some other way. Perhaps he/she gains fame from the competition or at least earns the respect of the bigger, stronger, faster opponent.
Probably the best underdog movie example that I can provide is the original Rocky movie. The reigning champion, Apollo Creed, essentially picks Rocky Balboa's name out of a hat, and offers him a chance at the title. Even with 24 hours to go before the fight, Rocky admits to himself that he can't win. Knowing that, he decides to try and "go the distance" during the fight. That means, he is going to try and complete all 15 rounds and leave the decision in the hands of the judges. By the end of the fight, everybody is rooting for Rocky to win. He doesn't, but he earns the respect of Apollo.
Other singular underdog characters from movies include Rudy from Rudy, Dusty Crophopper from Planes, and Daniel from The Karate Kid.
Most often though, Hollywood will generally make an underdog movie about an entire team being the underdog. Films that do that are Cool Runnings, Hoosiers, Miracle, The Longest Yard, The Bad News Bears, Major League, The Replacements, and The Mighty Ducks,