Hello Flowergirl -
I am not sure what your instructor's exact intention is regarding this question, but here's my interpretation:
I think crossing the line would be disclosing too much personal information or asking too much personal information that does not pertain to the diagnosis, treatment, etc. Or, this could include making arrangements for meetings outside the clinical setting, or doing personal errands, favors, etc. for the patient or their family.
The main thing I think they are trying to convey is that sticking to professional behavior/conversations/demeanor, etc. is what you want to do, and leave the intimate personal stuff at home.
I, too, am a nursing student, graduating in December from a BSN program, where the emphasis is on the "baccalaureate role" of the nurse, which simply means being as professional as possible in all situations, without seeming like a cold machine. This is all taught in the therapeutic communications classes I'm sure you will have.
I hope this helps - but asking for clarification of an assignment is one key to surviving all the assignments you will encounter as a student!