It's basically a semi-directional stationary slingshot. A gravitational slingshot. The angle(s) you come in at, the speed, the angle(s) you come out at, must all be calculated before a jump. Because if you miss by an inch, you miss by a few gazillion lightyears. Assuming it is not a standard gravity well like a celestial body (Round/globular) due to the shape of the relays, it limits what directions and receiving systems you can realistically aim at, which seems to be a Planned Hinderance (If we believe the Reavers built them as a way to manage sentients. "You go where we want you to go.").
In real life, this is done all the time. Well, as often as we need extra speed. Planets, moons, and asteroids have all been used for gravity assisted maneuvers. The math is difficult but can be done, the only limit is getting the spacecraft in the right spot at the right time, due to our slow no where near fraction of C propulsion methods.
Oh, and "If you pull the trigger on this, you're ruining someone's day somewhere and sometime. That is why you check your #$% targets! That is why you wait for the computer to give you a #$% firing solution! That is why, Serviceman Chung, we do not "eyeball it!" This is a weapon of mass destruction. You are not a cowboy shooting from the hip."