When the same MP3 file is transferred to your smartphone as an example, your player will use the album picture and other metadata information to display on-screen while playing and also giving you the feature to sort out or browse by artist, genre etc. You will notice the file size changes if you add cover picture, especially if you add large pictures. The data is saved on the MP3 file itself.
The cover art along with other metadata information are used by different audio or music players in different ways. The only thing that you have to do is bring up the media information screen and then the options will be accessible in the bottom-right after you right click on the art or VLC icon.
If you use VLC Media Player and if you want to display or add album art to any MP3 files, then just access media information options and either browse and put up an album art (also known as cover art) or try to download it automatically.