Triple option, when in the context of Navy football, refers to the offensive scheme that has been in place since the days of Paul Weatherbie, and remains in place under the current head coach, Paul Johnson - perhaps the only thing that didn't get replaced after Johnson took over duties on a team that had won two games in its last three years.
Navy uses the Triple option because it allows them to minimize the effect of their relatively small offensive line, and maximize the effect of the team's general athleticism and speed. Unfortunately, their use of the triple option is highly predictable- and as noted in hashbrownie's writeup- good college teams will eat the triple option alive.
But at Navy, triple option is more than the offensive scheme, it's also the promotional slogan for the team, replacing the oft-parodied and dubious "Expect to Win" slogan. All over Annapolis, you can find posters advertising the upcoming games with the tagline "NAVY FOOTBALL'S TRIPLE OPTION: TRADITIONS, TOUCHDOWNS, TAILGATERS". These posters usually have a large background picture of either the Brigade marching towards the stadium (tradition), the Navy quarterback slipping by the Army defensive line for a score (touchdowns), or Annapolis families barbequing and enjoying a game of catch with a football after the game (tailgaters).