If the technical terms put you off, just grasp the principle of orbital mechanics in the layman's way starting from the image of falling endlessly through space in the perfect orbit.
In real life (as simulated in Orbiter) even the most stable orbits have a highest and lowest point.
In atmospheric flight we use elevator and throttle to climb or dive.
In orbital flight the distances and speeds are way higher and you need to think in advance because the ship will not simply warp to another location when you fire your engines.
When you're at the highest point of your orbit, your ship is on the descending half of the orbit. This is the perfect time to correct the LOWEST point of the orbit as your momentum is already pulling you down to Earth, so to speak.
When you are at the lowest point of your orbit, your ship has the greatest velocity and with a little push from the OMS you can shift your Ap (highest point) a long way.
To do correction burns at the wrong part of the orbit is to waste a lot of fuel
Imagine a hyperbolic trajectory that is going at 10km/s at Pe (lowest point) at 150km altitude but you want to make your sci fi starship aerobrake instead (altitude 60-80km). You are already travelling 10km/s at 150km and what are the engines going to do, warp you 50km lower? It's impossible in physics or would require an ungodly amount of fuel to achieve possibly destroying the ship in the process due to G forces.
But since you have so much momentum it's simple to just let the ship go around to Ap one more time, reach the highest point, and then correct your PeA to intersect with the upper atmosphere to aerobrake.
In your ISS example, just wait until you're at the descending part of the orbit, watch the PeT timer, and when you're at the lowest point fire retro to reduce your speed and thus the ship will not rise as high (Aim using ApA display)
See, playing in space is fun :3