I'm not sure if you are talking about a graduate year program, ie first year as RN or postgraduate study, so I will answer both.
A graduate year program is offered by hospitals etc to first year RN graduates. It is aimed at being a supportive transition to practice program with relevant study days incorporated in the program. No you don't have to do one, but they are very helpful in helping you transition from being a student into a practicing nurse.
Post graduate courses can be either at certificate level or diploma level, if you want to work as a manager in a specialty area then you would opt for the diploma otherwise certificate level is fine, and certificate level will take you to clinical nurse specialist. Post graduate study gives you skills and knowledge relevant to that specialist clinical area. You do not need it to work in theatre or renal, but it is highly regarded and you make yourself more employable by having qualifications in specialty areas.
I found that universities pushed postgraduate study, then when you were doing the postgrad they pushed masters, and when you were doing a masters they were encouraging you to PhD.
Think about where you want to go, how to get there and how long the study is going to take and the amount of money it's going to cost before you sign up for anything.