Andersen is a patronymic name. It originally indicated that the person identified with this name was the son of a man named Anders.

Online study material to learn about Norwegian naming practices and patterns.

http://homepages.rootsweb.ancestry.com/~norway/na12.html
http://www.nndata.no/home/jborgos/names.htm
http://www.norwayheritage.com/norwegian-names.htm
http://www.nndata.no/home/jborgos/farms.htm

Patronymic names were common in a number of European countries.