Why is the symbol Ar used in the electron configuration of potassium, and what does it represent?

It represents the noble gas that precedes the period before Potassium.

Explanation:

Period before potassium is 3, the noble gas in that period is Ar (Argon). So when condensing the electron configuration of Potassium, Argon can account for 18 electrons instead of writing out 18 electrons in full form from 1s2, 2s2 etc.