Andersson is an extremely common surname in countries such as Sweden, and Anders is an extremely common first name aswell. Andersson simply means Anders' son (or the son of Anders). A lot of people dropped the first "s" when migrating to North America, for example - the same happened to surnames such as Johnsson, Karlsson, etc.

Common name variants on the proto-Germanic word "Ander"/"Antheraz" include Andrew, Andy, Andre, Andreas, Drew, Deandre, and Deandra.

Bear in mind this is unrelated to the Greek word "Anthro."

Edit: I thought proto-Germanic "Ander" and Greek "Anthro" were related but when I wrote this post I couldn't find attestations to that effect, so in my post I said the words were unrelated. Follow up research says the words do have a common root.