Parián

Question

In my hometown there is a Mexican restaurant called "El Parián". Up until today I always figured that it was named after a town in Mexico. But today I was reading a story (El Medio Gallito) to a group of children where one page is written in English and the other in Spanish. It mentioned el parián and the English translation on the other page inferred that it was the market in the town square.

Is it really referring to a town, or it is a local term for market, or am I totally off the mark here'