Adventure stories are among the primordial genres, those stories that were told around cooking fires when humans first learned what storytelling was all about. Tales of distant lands, heroes, conflicts and triumphs are the stuff of adventure in theater and literature - the novels of Jules Verne are prime examples - and with the advent of film, all those elements easily and naturally made the transition to the movies.
Adventure stories often follow the exploits of a protagonist who fits into the famous "Hero's Journey" model, an inexperienced adventurer who, through a series of challenges and victories, is transformed into a hero. Think of Luke Skywalker in Star Wars or Frodo Baggins in The Lord of the Rings. The young hero overcomes obstacles, and with the help of his friends, becomes something much bigger than he once was and often saves the world (or worlds) in the process.
Adventure movies usually have prominent elements of action in them, but the action sits in the framework of the overall journey or quest. Indiana Jones in Raiders of the Lost Ark engages in numerous thrilling action sequences, but the quest for the ark is the thread that keeps the story moving forward.