John Farley's explanation is perfect, but let me try a slightly different tack that I think compliments John's:
The concept is energy management, almost identical to the helo concept of hovering in ground effect to accelerate while attempting a barrier takeoff. While trundeling down the deck, the Harrier can devote almost all its thrust to accelerating the beast to some appreciable forward speed. If it were resting on its plume of air, literally nothing would be left to accelerate it. The ramp lip points upward so some of the ground speed (deckspeed) is converted to climb that allows quite some lofting of the aircraft. This lofting buys time to let the aircraft transition to forward flight, and negates the problem of down deck angle in a pitching sea, as John so well puts it.
Helos could use exactly the same technique, if they were so vastly overloaded. Wisely, we have not been so burdened, yet.
Look for this jump technique for V-22, as its rolling takeoff weight, as compared to hover weight, creates a compelling argument for a rolling takeoff.