If something is stable, it is not likely to change or come to an end suddenly.

If someone has a stable personality, they are calm and reasonable and their mood does not change suddenly.

You can describe someone who is seriously ill as stable when their condition has stopped getting worse.

Chemical substances are described as stable when they tend to remain in the same chemical or atomic state.

If an object is stable, it is firmly fixed in position and is not likely to move or fall.

A stable or stables is a building in which horses are kept.

A stable or stables is an organization that breeds and trains horses for racing.

When horses are stabled, they are put into a stable.

You can say that someone has a stable of people when they manage and promote the careers of that group of people.

If you say that someone has closed or shut the stable door after the horse has bolted, you mean that they have tried to prevent something happening but they have done so too late to prevent damage being done.