EU residence document
The EU residence document is proof that that you meet the conditions for residence under EU legislation and therefore have the right to reside and study in Denmark.

CPR Number
In Denmark each person has a personal registration number, which is called a CPR number. CPR stands for Central Person Register.
The CPR number is essential in relation to any contact with the Danish authorities and especially in connection to tax and social security issues.
The CPR-number gives you the right to use the Danish health care system.

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A temporary health insurance card
The document is your temporary health insurance card until you receive the actual card. It contains the name, address and phone number of your doctor. Until you receive your actual health insurance card, you must bring the temporary document if you are going to the doctor, hospital or dentist.

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The actual yellow health insurance card
About 14 days after your entry has been registered, you will receive a yellow health insurance card (sundhedskort) by post (please have your name on your mailbox). The card carries your Danish CPR-number (social security number). You are advised to always carry your yellow health insurance card with you as you will need to use it when contacting your doctor, hospitals and dentists.
Read about healthcare in Denmark here

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NemID is your personal secure login for digital contact with public authorities, for your Digital Post, for netbanking and a wide range of online self-service solutions. You log on with NemID via your personal user-ID, a personal password, and a code card with one-time passwords on. Your NemID is set up by Citizen Service (Borgerservice) when you do your registrations.
Then, after 3-11 days, you will receive two letters, one with your code card and one with an activation password which you must use in order to activate your NemID.
Read more about NemID here