DAPI stands for 4′,6-diamidino-2-phenylindole and it is a fluorescent stain that binds to DNA in the nucleus. It is a stain used very often in fluorescence microscopy, when excited with ultraviolet light DAPI emits a blue light. This makes the stain very popular in fluorescence microscopy making the nuclei visible in a blue colour. As an example in the picture below there are various cells which you can distinguish by the blue nuclei and the cytoskeleton stained with another dye that emits a greenĀ  light. The picture was taken from thermofisher.

Mouse Anti Beta-Tubulin Monoclonal Antibody Nuclei (blue)