Excellent question. First off, I completely agree with what was mentioned earlier by Malftap: They allowed me to do this stuff because I was dedicate to learning. You have to go in wanting to learn the stuff and not go in just wanting something to put on your application. So you can actually end up doing a lot and like I said it all depends upon the hospital." I only want to add two things: (1) you are not trained or licensed to give any medical or psychiatric help so don't do it, and (2) you are REALLY there to prepare yourself emotionally for medicine by interacting with patients and seeing if you can discover the value in working with them.
To directly answer your question, you should expect to run errands or help patients in a non-medical manner. More specifically, that may mean taking samples to the lab or helping a patient communicate with a family member or friend if visitors are not permitted. In my case, I volunteer at in an emergency department at a county hospital in Oakland, California; county hospitals need help so I greatly encourage you to volunteer there instead of at a private hospital. Moreover, I serve as a Spanish translator and help patients communicate with everyone from the triage desk up to the physician's H&P; knowing another language will make you very popular if the staff needs you to communicate with patients. Lastly, if the emergency room is not your thing, try the cardiology lab. There you can learn about the heart, EKGs, and echocardiography. Good Luck.