Okay, so imagine you are playing with two toys - one is a big ball and the other is a smaller ball tied to a piece of string. You hold the big ball in one hand and tie the string around it, and then you hold onto the string with your other hand so the small ball is hanging down.
Now, the kozai mechanism is like what happens when you start moving your hands around in circles. When you do this, the small ball on the string starts swinging back and forth in a different way. It doesn't just swing straight back and forth anymore, it starts going in circles too!
Scientists use the kozai mechanism to help explain how two big objects in space - like planets - can affect each other's orbits. Just like how you moving your hands in circles affects how the smaller ball swings, the gravity of one planet can affect the orbit of another planet.
So, if two planets are orbiting around a star, and one of them is much smaller than the other, the smaller one's orbit can start to change because of the bigger one's gravity. It doesn't just go in a straight line anymore, it starts going up and down too - just like how the small ball on the string went in circles when you moved your hands.
Scientists like to study the kozai mechanism because it helps them understand how planets move and can even help them find new planets in our galaxy!