Embedded artwork basically means that an image (I prefer jpeg's) is encoded into the mp3 file tag. This means it is now part of that mp3 file. No matter what program you use, it will always show the correct artwork for that music file when it is playing.
iTunes does not embed album art into the files. You can do it manually  through iTunes, but there is no function available to make it  automatically do it. Instead, iTunes stores its artwork in some ****ed up database folder structure that is almost impossible to figure out. It works fine if you are using iTunes, but as soon as you try another program, your artwork will not show up. That is because the artwork is stored in the weird folder structure rather than directly in the mp3 file itself.
About 5 years ago I went through the tedious process of embedding artwork in all my files, and continue to do the same today. I have yet to have one program or app not see the correct artwork. Embedded artwork is the best way to go. It is future proof and ensures that no matter what program or app you use, the artwork you want to see will show up.
Now a days there are many automatic embedders that do a good job. I prefer to do it manually using mp3tag, but there are other options. You mentioned you use iTunes. I would recommend trying something like the below link. It will use the iTunes artwork and automatically embed it for you. I have not tried it myself, but it seems to have a good reputation.
Maximized Software iCoverArt: Embed Album Cover Art Into Song Files in iTunes