In a very general sense, the role is simply that of a (hopefully) cooperative part.Is there a role you play as a part within the whole?
Hopeful in the sense that the quality of the role depends on behaviors or attitides that help foster that connection.
For instance, if I simply say "I am a father", it tells of my role but it doesn't say anything about what sort of dad I am (in what way I am good/bad, effective/useless etc).