Acid-fast
Acid-fastness is a physical property of certain bacteria (and, less commonly, protozoa), specifically their resistance to decolorization by acids during staining procedures.
Acid-fast organisms are easy to characterize using standard microbiological techniques (e.g. Gram stain - if an acid-fast bacillus (AFB) was gram stained, the result would be an abnormal gram positive organism, which would indicate that further testing wasn't necessary), though they can be stained using concentrated dyes, particularly when the staining process is combined with heat. Once stained, these organisms resist the dilute acid and/or ethanol-based de-colorization procedures common in many staining protocols, hence the name acid-fast.