Travel insurance usually comes with health insurance for the duration of your trip. If you live in a country which has good state-provided healthcare, and travel to a country which does not have a recipicalreciprocal arrangement, you will normally have to pay all medical costs you incur.
If you accidentally slip and break a leg, or suffer a heart attack, you can end up with very expensive medialmedical bill. IIRC, for the US, coverage of $1 million is recommended. If you have a full-leg cast as a result of injury, you may need to fly back home in first-class. This is so that you can keep your legs straight. The travel insurance should cover buying a first-class ticket for you (and possibly one of your travel companions). Doing this on your own dime may be costly.
Should you end up an a coma, and need to be medically repatriated across continents, this is very expensive.
NB. This answer is not inviting a discussion on private vs state health coverage.