Amager Fælled is a former military area, which is a protected place today. It is a popular place to go for a long walk with the family and you can do different activities, including playing football at one of the football courts in the area.
It is a good place to watch the wildlife, get some fresh air and clear your mind. There are several lakes in Amager Fælled. If you want a very beautiful view over the whole area, you should go to on of the small hills, called "De tre høje". Here you'll have a great view over Amager Fælled, and you can see some of the higher buildings in other parts of Copenhagen.
This is a great place to go, when you wanna explore the nature of Copenhagen - and you won't get a feeling that you walking around very close to the heart of Copenhagen.