If you are studying for a master's degree, Ph.D, MD, or JD, you are going to "graduate school". If you are going to graduate school, you are a "grad student." Speaking casually, all the stuff that a grad student needs to do an be called "grad stuff". So, "grad stuff" could involve studying your subject, doing experiments, teaching undergraduates, and writing your thesis.
So, if I ask a grad student,
"Hey, do you want to go hang out tonight?"
She might say:
"Nah, [I have] too much grad stuff."
So, it means that the work that she needs to do at graduate school is keeping her busy, and she doesn't have the time to go hang out with me.