What is Anmeldung ?

Anmeldung (which means "To Register") is simply the fact of registering yourself as living at a specific address in Germany.
When doing so, you will be given the “Anmeldungbescheinigung” , ( “Registration certificate”).

Every German citizen or new comer in Germany is supposed to register within 14 days after moving into a new house or flat.
But if you stay in Germany for less than 4months, then you dont need an Anmeldung. You are considered a tourist and dont need to register
This piece of paper is required when opening a bank account, getting electricity or gas, getting a phone contract, and also to obtain a tax number.

When doing the Anmeldung you need your ID, & your tenancy or sublet agreement. You will need to fill a form called “Anmeldung bei einer Meldebehörde” that you get at any Bürgeramt or Bezirksamt(Citizens administration office) in your city.

You will sit down with a city employee who will type in all the info you provided into the computer. 
It should only last about 5min and You are done with the Anmeldung.  

The ceritificate is mailed to your address within 2 weeks or more in some cities.

Source : 

http://www.settle-in-berlin.com/anmeldung/#ixzz4XG4vxhQh