Don't be fooled by the name - although its important to carry with you whilst in Europe - it's not Insurance!...
The EHIC entitles you to reduced cost (or sometimes free) healthcare where treatment becomes necessary during a temporary visit to countries of the European Economic Area or Switzerland. The card is only valid for treatment offered under the state healthcare schemes operating in these countries; it gives you access to treatment under the same terms as people who live in the country you are visiting.
The EHIC is not a substitute for travel insurance. Since it may not cover all health costs and never covers repatriation costs, you are advised to take out a travel insurance policy in addition to the EHIC. Travel insurance also provides cover for many other aspects over and above emergency medical, including cover for personal liability, baggage, missed departure etc.
Further information, including a full list of countries covered along with details of their "health systems" can be found online at www.nhs.uk/healthcareabroad. It is strongly advised that you take this and your travel insurance information with you when you travel, as both tell you what to do if treatment does become necessary during your trip.