Okay, let's get into some explanations of the lore behind jets.
First thing's first: We call them "jets," but that's really just a useful shorthand -- a bastardization, if you will. A better term for the jets in Legions would be "thrusters," since that's what they provide: thrust in a given direction. The thrusters on each suit don't take in air in order to expel air and push the wearer up; thus, they are not "jets." In fact, the only displacement of air that happens when you're flying around in a suit is a result of the cushion beneath it, but we'll get to that.
The thrusters attached to each suit are officially called "Gravity Negation / Reserve Lift" systems, or GNRLs ("generals" when spoken). This is an accurate, if incomplete, description of the systems' functionality: They do indeed negate gravity, but they do so in very small pockets within each nacelle. Within those pockets, gravitons are manipulated by the suit's systems, generating artificial gravity wells that pull in controlled directions. These wells are powerful, but just like the gravity we experience every day, they must overcome the potential energy of the suit itself -- objects at rest, after all, tend to want to stay at rest.
The other half of the GNRL system is the "Reserve Lift" component. It refers to the semi-solid "gravity shell" that's generated beneath the suit whenever the thrusters are powered on. This shell is comprised of two layers of gravitons generating an immensely dense gravity pocket between them, which shoves all matter within the pocket outside of it. This creates a fairly decent (though not run-away-intense) air vortex beneath the player as the gravity fights to expel the air, and nature fights to fill the vacuum.
Anyways, when you fire up your GNRL thrusters (but we'll just call them "jets," because it's easier), you're activating that gravity pocket/cushion beneath you, which negates friction handily. There's also a slight ability to control the angle of the shell, which is how you're able to move in the four cardinal directions.
But the real action happens when you use your "up-jets" or "down-jets," which are really just terms used to describe activating the graviton pockets within each nacelle. As the suit overcomes its potential energy, you start soaring higher and higher with increasing speed, until you run out of energy and your jets shut down completely. Add in some energy management and the beautiful forces of inertia, and you get skiing!
The last piece of the puzzle is Overdrive. Overdrive shifts the two graviton layers in the shell from underneath you to in front of you, and sets them both in the same direction instead of opposing each other. When this happens, instead of the two directions cancelling each other out like electric charges, they double up, and the suit is propelled forward at incredible speeds. Unfortunately, the suit must then deal with some serious, literal G-forces that are constantly changing direction as it tries to compensate for slight variations in trajectory, which makes the wearer bounce around inside the suit like ping bong balls in a Stride gum commercial. The body simply isn't equipped to handle those sorts of forces, and horrible stuff starts to happen inside of it -- tendons start snapping, bones vibrate and even shatter, organs rip and tear themselves apart; it ain't pretty. Hence, the health depletion.
Anyways, that's how your jets work. Now go forth, and ski!