I have seen two causes of this issue (there may be more, but these are the two I have experienced).
First cause (this happened on my daughter's phone): Restoring a backup from a phone backup, and having iTunes set to "Manually manage music and videos". That results in the music app thinking the music and artwork is there (i.e., database restored, so lists it in music app) but the tracks themselves aren't on the phone. To fix this, connect to itunes and manually move music to the phone (per normal process using "manually manage music and videos").
The second cause, which I had on my 5S: There appears to be a bug in either iTunes or iOS7 Music App related to the handling of "Artist" values that contain special characters like colon (":"), hyphen ("-"), ampersand ("&"), or parenthesis ("()"). To fix this, go into your itunes track list and look for tracks where the "Artist" or "Album Artist" field contains special characters, temporarily remove those special characters, and re-sync the phone. This completely fixed all my album art issues on my 5S. Hopefully Apple will address this bug in a future release, and then the special characters can be used again.