In some games, stars are used to represent a player's experience level. Does anyone know the origin of why people do this?
I guess it might be because it represents reaching another milestone but I can't find proof of this.
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Short answer: Around the world the star is iconic for a special feat or rating therefore making it a good symbol for experience or awards in video games.
Long answer: Stars have been used in the army for many many years to indicate the top military ranks. For example: in the US, stars are awarded from being a senior-commander (1-star) up to the rank of general (5-stars). Wikipedia article about military ranks around the world.
Also, as Patomas points out, the star system is used as a rating system in a lot of different contexts. Think of the Michelin-star guide for the top restaurants around the world, or hotel ratings. Another Wikipedia article, about Star classification
In many cultures around the world stars seem to have become a representation of a special feat, something you earned through hard work. Therefore making it a perfect candidate for using it as a mark of experience in videogames.
Although some games may use that as an indicator, and I can't think of any right now, stars are rooted in our mind as level markers from past experiences, for instance, hotels, restaurants (although they use forks), review for movies on news papers and magazines etc.
The most common is of course the hotels. The 5 star rating system for hotels seems to have started around 1958, and this is the meaning that we usually associate with this ranking system, quality and excellence.