This is an old name for what would be called a “pharmacist” today.
I’m not saying it was a pharmacist, because usage of the name stretches back thousands of years, and we wouldn’t call what they did back then “pharmacy.” However, it filled the same basic role.
Apothecaries prepared medicines, old ingredients, and performed some medical procedures.
The etymology of the word, however, is more general:
The term “apothecary” derives from the Ancient Greek ἀποθήκη (apothḗkē, “a repository, storehouse”) via Latin apotheca (“repository, storehouse, warehouse”, cf. bodega), Medieval Latin apothecarius (“storekeeper”), and eventually Old French apotecaire.
Technically, an “apothecary” can just be a store or storekeeper, which is more common today. The word is interesting, and it’s used more as a branding device to inspire nostalgia than anything else.