The yellow health insurance card (sundhedskort) is your documentation that you are entitled to the services offered under the Danish national health insurance scheme. If your heath insurance card is lost or broken you can order a new card.
If you need medical treatment during travels in the EU, Norway, Iceland, Liechtenstein (EEA), or Switzerland you will have to use the Blue European health insurance card.
The special health insurance card is issued to citizens who do not live in Denmark but are socially insured in the country. The special health insurance card gives you the right to use the Danish healthcare services on the same terms as citizens who live in Denmark.