The guys that founded the University of Copenhagen explained what Anthropology is in 1647. They basically said that it is the science that “treats of humans”. The Wikipedia article on anthropology goes a bit further and divides the field into two categories. The first one is Anatomy, which is focused on the body parts. The second one is Psychology, which is focused on the soul.
Of course, as soon as you deal with humans, which is a key focus of Service Design, you are interested in what anthropology and psychology can bring to make services less frustrating and more fun for the humans who use them.
Going further
This article is part of the book "A Tiny History of Service Design, " a tiny two-hour read that goes through the historical events that created what Service Design is today.