"Dragon liver, seventeen Sickles an ounce, they're mad...."
-- woman outside the Apothecary in Diagon Alley (PS5, original text)
The Apothecary is a shop selling potion ingredients in Diagon Alley. It is a fascinating place crammed with all sorts of interesting things. There are barrels of slimy stuff lined up on the floor and jars of all sorts of powders, herbs, and the like along the walls. Bundles of feathers, fangs, and claws hang from the ceiling. The whole place smells very bad, a mixture of bad eggs and rotten cabbage (PS5). A barrel of dragon dung sits outside (CS4).
In HBP, Bellatrix Lestrange's poster is seen "sneering from the front of the nearest apothecary," which suggests that there are more than one of these shops in Diagon Alley (HBP6). However, in that same passage, we read:
"Everyone all right?" said Mrs. Weasley. "Got your robes? Right then, we can pop in at the Apothecary and Eeylops on the way to Fred and George's... stick close, now..."
which suggests that there is only one and that it's actually called the Apothecary (note the capital letter). In the Pottermore version of Diagon Alley, there was only one Apothecary, located just past the cauldron shop (shown focused in the image).
The films and the theme park name this shop Slug and Jiggers (PS/f, WWHP).