organisms that thrive under highly acidic conditions (usually at pH 2.0 or below)

An acidophile is an extremophile organism which thrives in extremely acidic conditions. What "acidic" usually means here is environments at pH 2.0 or below. These organisms can be found in different branches of the tree of life, including Archaea, Bacteria, and a few eukaryotes.

Inside the organisms, their cells are at a normal pH. They have evolved mechanisms which pump protons (H+) out of the intracellular space in order to keep the cytoplasm at or near neutral pH.