The KIPP students who graduated from college were not the academic stars but the workhorses, the ones who plugged away at problems and resolved to do better.
For example, if you're learning how to cook, but you're having problems making good dishes, you decide to keep trying, however, you keep plugging away in order to become a better cook.
" To plug (plug) away" means to continue to do something, especially to continue to do something that may not seem important that you may have to do over and over again, but that has to be done.