Shorter queues for non-essential procedures, nicer facilities (e.g. private rooms instead of wards), doctors who speak your language of preference, doctors available by videocall, healthcare whilst abroad included, that kind of thing.

Nothing strictly necessary, by definition, but lots of perks.

It's worth bearing in mind too that private healthcare is also _much_ cheaper in Europe than the US. In Spain for example I can get private healthcare + dental with zero copay for about €70 a month.

In Italy public healthcare provides everything, even dentist, but waiting list are really, really long. Obvisosly, an emergency is managed immediately (a broken bone will be fixed immediately at no cost without asking anything), also cancer and health issues with tight time constraint, for everything else not urgent you have to wait, sometimes a lot. Also health care quality is a lot different from place to place, in north Italy is quite good, in other places not at all. There's a lot of national "health turism", as we call it, people moving for hundreds of km, usually from south to north Italy, to find a better health care. So, if you want/need to "skip the line", you have to pay private healthcare, otherwise you wait, if you are lucky a few days, if not also more than a year. For my last medical examination to my eyes, nothing serious, just a check, I wait about a month. Of course, COVID pandemic aside.