So, imagine you are playing with a toy spaceship and you want it to stay in the same place in the air for a long time. But some annoying things keep making it move around, like wind or other toys bumping into it.
That's how it is for real spaceships and planets too! There are lots of things in space that can make their orbits change over time, like other planets and moons pulling on them with their gravity, or even the sun's gravity changing as it moves through space.
Orbital perturbation analysis is a fancy way of trying to predict and understand how these changes will happen. Scientists use math and computer programs to try to figure out how all the different factors affecting an orbit will change it over time.
Just like you might use your brain to try to decide how hard to throw a ball to make it land in a certain spot, scientists use these tools to try to predict and control where spaceships or planets will go in space. It's like a big puzzle that they have to solve in order to make sure everything stays safe and works as planned.