An acidophile (or acidophil, or, as an adjectival form, acidophilic) describes is a term used by histologists to describe a particular staining pattern of cells and tissues when using haematoxylin and eosin stains. Specifically, the name refers to structures which "love" acid, and take it up readily.
It describes the microscopic appearance of cells and tissues, as seen down the microscope, after a histological section has been stained with an acidicdye. The most common such dye is eosin, which stains acidophilic substances red and is the source of the related term eosinophilic. Note that a single cell can have both acidophilic substances/organelles and basophilic substances/organelles, albeit some have historically had so much of one stain that the cell itself is called a eosinophil.