Cominciamo con i professionisti.

Copre le spese mediche
Una polizza di assicurazione sanitaria privata copre alcune spese mediche che il sistema sanitario pubblico o Medicare non copre.

It covers (some) hospital expenses
In the event that you'll require hospitalization, a private insurance policy could cover some of your expenses, and you'll be treated like a private patient.

And now for the cons - and there's a big one:

The cost
This will be a real problem if you're already in poor health and don't have any kind of group coverage. Usually, individual health insurance policies can cost around a few 100s of dollars a month.