If something is done stably, it is done in a way that is not likely to change or fail.
Doing something stably is a good thing because it means it is done in a strong and reliable way.
Examples:
She rides her bike stably without falling.
The tower stands stably in the wind.
He works stably and never makes mistakes.
The cat sleeps stably on the windowsill.
The superhero lands stably after jumping from the building.
The house is built stably so it won't fall down easily.