I think they are speaking of the Oberth Effect: http://en.wikipedia.org/wiki/Oberth_effect about which I know nearly nothing, but the multiplier at the end of the Wikipedia example is 3.3.

In brief, you let a planet pull you in to its gravity well, then while you are going very fast burn your fuel to get your Δv.

At this point my physics falls apart. You either…

1) Gain the energy from the propellent coming down and not having to go back up. (f=ma doesn't help me here)

2) Gain extra energy because the rocket force is constant and with a greater 'v' the kinetic energy is greater. (says whose frame of reference?)

3) Gain energy because you balance some equation and realize you left the exhaust at a lower altitude. (Dr. Carl Bender tried to pull this stuff on me in freshman physics. It looked good on him.)