It is roughly what we would now call a pharmacist or a drug store (if you are talking about the shop in general). In other words, it is the term that they used back then for a person or a shop where you could buy the things that passed for medicine back in those days.
In Act V, Scene 1, Romeo goes and buys his poison from an apothecary. You can see that poison is not something he is supposed to be selling. He says he'll only sell it because he's so poor (which is why Romeo picked him). He is supposed to be selling stuff that they thought could cure sickness.
As the previous respondant indicated an apothecary was basically what we know today as a pharmacist. It was a term used for medical specialist who made and dispensed medical knowledge and supplies. The apothecary was also known to help during surgeries and child birth. By the end of the 19th century the job of the apothecary had become specialized to only working with medications.
The first historical mention of the word apothecary was in the Old Testament in the book of Exodus. "According to Sharif Kaf al-Ghazal and S. Hadzovic, the first apothecary shops were founded during the Middle Ages in Baghdad."