The subtitles of both A New Hope and Return of the Jedi are each interpretable in two ways. (In the case of Jedi, there are both the return of the Jedi order from extinction, with Luke's declaration of victory; then shortly thereafter comes the return of one individual Jedi, Anakin Skywalker, from the Dark Side. The name of Revenge of the Sith—modeled after that of Return of the Jedi potentially features the same double meaning of single versus collective.) With Episode IV, the two hopes that appear are Luke Skywalker and the events of the film—particularly the climactic destruction of the Death Star.
The more obvious one is Luke, who joins the Rebellion, achieves the destruction of the Death Star, and is clearly tapped to become a future Jedi knight. In both Episode V and Episode VI, Obi-Wan (incorrectly—and Yoda contradicts Kenobi in both cases) states that Luke is the only hope of the Jedi order—and thus for the galactic civilization itself. However, the whole framework of the first movie is that the Rebel Alliance is on the verge on a titanic breakthrough in their battle against the Empire. According to the opening scroll, the rebels have just won their first battle against the Empire, and the plans stolen during the battle are described as: "the stolen plans that can save her people and restore freedom to the galaxy."