To make something steady and not change.
Stabilize is a good thing. It means to make something safe and not moving.
Examples:
I need to stabilize the wobbly table.
The doctor helps stabilize the sick man.
She tries to stabilize the shaky tower.
I need to stabilize my bike so it won't fall over.
The superhero stabilized the shaking building with his superpowers.
We need to stabilize the situation before it gets worse.