What does mean by the $\text{stable}$ action of a Galois group $\text{Gal}(\bar K/K)$ on a set $X$?

Question

What does mean by the $\text{stable}$ action of a Galois group $\text{Gal}(\bar K/K)$ on a set $X$?

i.e., when we say an action of the Galois group is $\text{stable}$ ?

Please explain it and perhaps if possible with an example.