The answer is virtually anything and everything. A lot of nurses are very highly trained and they might let you shadow them- ask.
Be wary of anything involving medicines or anything similarly prescribed. When a nurse is administering these they should be not be disturbed as it increases the risk of an error. I'd include things like IV fluids and supplemental oxygen in this also. Learn by all means but seek supervision and guidance if you are involved in using them.
The nature of nursing very much depends on where you are placed at the time. Some wards or departments are sort of 'relaxed': 6 hourly observations, patients who are otherwise on the mend, greater emphasis on good old fashioned care. Others contain acutely unwell patients who will require lots of nursing input almost around the clock. If you get the chance, resus or critical care will show you the absolute peak of the nursing art and profession. If you can manage working in those places, you will thrive anywhere.
A lot of nursing tasks are best learned by repetition. I do not think there is much substitute for this really so when you are on placement get stuck in with both hands. Ask if there is any supplementary training on offer in your hospital- I was amazed to learn that not all nurses qualify whilst being trained to perform venepuncture, cannulation or place catheters- these are all standard fare in my view and a portion of HCAs can do these so surely nurses should at least know how to do them also.