It's the transliteration of the French word salon. It is equivalent to the English word saloon or salon (alternative spellings). The French word probably is derived from the Italian word salone meaning a large living area in the house or more generally a place where people gather to socialize. In China, the hairdresser's is often an unofficial social gathering place for especially neighbours, so it's not surprising that the word has been extended to mean hairdresser's in Chinese.
Note that 沙龙 doesn't always have to refer to a hairdresser's. It is also used in the way salon is used in English and French, i.e. a gathering place for socialization. For example, a 英语沙龙 is a place for people to gather and practise their English. No hairdressing involved there!
As to why people would borrow a term from a different language when there is already an existing one in the source language, there could be many reasons - fashion, western influence and convenience are just some of them. A good example is the word for a (train/subway) station in Japanese. The Japanese term for it is 駅 (えき, eki), but there are many places, even on official maps, where it is replaced by ステーション (sutēshon). I can't tell you the exact reason without doing some major research into the phenomenon.