This depends on what program you're using. Some programs can only read certain files exclusive to that program, such as .psd files can usually only be read in Photoshop or other adobe programs. Many fields of work (Journalism, the Arts, Design, etc.) ask for .psd files to be converted to either .png, .jpg, or .tiff so that it can be seen on many other platforms.
For images especially, files are more compatible either on a program or printed. for example, .png files are good for storing color data from computer to computer, but if you print a .png file, the quality is poor. hence it's recommended to save files you want to print for designs as .jpeg, because .jpeg can more easily be printed and will then be presented at a high quality.
Sometimes color quality changes depending on CMYK as well but that's a whole other ball of wax.
