If you are travelling away from your home country (where you have medical cover presumably), you need travel insurance to cover you in the event of illness/accident - basically - anything medical. Your medical cover at home will not have the least bit of interest once you leave the country.
That's just the medical part of it, which if things got bad could leave you with a bill of several million dollars.
Other things that insurance covers:-
Lost luggage - missed departure - delayed departure - lost money - lost passports - public liability (you could get sued for x million $ for accidentally hurting somebody) - neccessary cancelation before departure owing to your illness or that other a close relative..... the list is quite large.
When I book a cruise the booking form asks me whether I want their insurance, and if not then I must specify with whom I have bought insurance and what the policy number is. My cruise line does not want to be lumbered with me in the middle of the ocean wanting an airlift but without insurance (or a $1 million credit card handy!!!!)
Peace of mind.