The primary responsibility of the Canadian Armed Forces (of which the Navy is a part), is the defence of Canada. After that, there is a declining order of responsibilities (defence of North America, defence of NATO, etc) all the way down to, whatever the government decides it wants us to do. Nevertheless, the RCN is a "blue water" navy, meaning we operate internationally as best we can (can be difficult sometimes considering our size). We operate as part of NATO and other international maritime task groups.
Thankfully, we have not lost any personnel in the last few decades to outright combat against an armed enemy, but we have lost a few in training accidents and unfortunate occurrences in foreign ports. We've even had at least one sailor lost at sea, but we don't know if that was a suicide or not. Frankly, our most dangerous opponent of late is the sea itself.
Once you're in and have completed your obligatory service, you will be eligible to apply for the Military Medical Training Program (MMTP), which will send you to a Canadian medical school (although you have to get accepted to it on your own) and seek to qualify you as an MD. This will incur further obligatory service, but you get to go to medical school on the Queen's dime (all tuition, books and equipment are paid for) and at full salary (likely as a Lt(N)). Should you choose the direct route (i.e. apply to medical school now), the Medical Officer Training Program (MOTP) is available, which is similar to the MMTP, but your salary while in school will likely be considerably less.