Final answer:
Fluorescent stains bind to molecules in cells and emit visible light when excited by UV light, allowing observation under a fluorescence microscope.
Step-by-step explanation:
The stains that bind to specific molecules within cells and emit light when viewed using a fluorescence microscope are called fluorescent stains. These stains, or fluorochromes, are absorbed by the cells and emit a visible light when excited by light of a particular wavelength, usually ultraviolet (UV) light. Examples of such stains include 4',6'-diamidino-2-phenylindole (DAPI), which stains nuclei, and fluorescein isothiocyanate (FITC), commonly used to label antibodies.