Commençons par les avantages.

Elle couvre les frais médicaux Une police d'assurance maladie privée couvre certains frais médicaux que le système de santé public ou Medicare ne couvre pas.

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.