The rising action, in a narrative, is the period of action after the exposition and general introduction of characters and conflicts, but before the story's climax.
Initially, the rising action was a slow to develop part of any play or story, as the climax was often followed by a swift denouement and ending; often times, stories such as Marlowe's Faust and Edgar Allan Poe's The Cask of Amontillado would continually rise in tension and setting before erupting into a glorious finale.
Lately, with the recent push for narrative invention and stylistic individuality, rising action has seen a lot of different touches added to it. In Quentin Tarantino's Pulp Fiction, most of the movie's rising action occurs after the climaxes, as a smart way of revealing characters and their motives and the various interwoven storylines of the plot. Another movie, Christopher Nolan's Memento, takes full advantage of rising action by shooting in reverse. Thus, the entire movie is a climax followed by the rising action which leads to another climax.
Both of these movies make liberal use of in media res storytelling - beginning in the middle and then expositing with flashbacks and alternate stories. This contrasts starkly with the more direct form of rising action in plays prior, with soliloquies and asides to the audience to further the plot from within without giving away details to all of the characters.
Rising action is considered an important time to make readers feel for the characters they have been introduced to, by showing them interact with others. Sometimes the rising action is merely a way to maximize the number of questions an audience might have - Bryan Singer's The Usual Suspects continually interrupts its rising action narrative (being told in a flashback) with the seperate storyline of Verbal Kent in the police station. The audience gets to asks questions through the main detective in the case, and when the final climax comes, we get both storylines resolved in one fell swoop.
Rising action: use it well, young writers, and you can sell just about anything.