Stardom is the condition of being a star — famous as a performer, known by people who have never met you. Singers, actors, athletes. It is not the talent and it is not the money; it is the state of being that famous, the whole world you enter once it happens.

It is an uncountable noun, so no 'a' and no plural. It shows up most often in a small set of phrases about the moment of arriving: rise to stardom, shoot to stardom, catapulted to stardom, on the road to stardom. That tells you something about how the word is used — it is usually about the journey up rather than about sitting at the top.

The feeling is often double. Writers use stardom for glamour, but just as often for what it costs: the loneliness, the pressure, the loss of a private life. 'She was not ready for stardom' is a common shape of sentence, and it is sympathetic, not sneering.