What is an automorphism of a database instance?

The following definition is from the book Relational Database Theory by Atzeni and De Antonellis:

Definition: An automorphism of a database instance r is a partial function

        h : D --> D
where D is the domain of the database r such that 1) the partial function h is a permutation of the active domain D_r, and 2) when we extend its definition to tuples, relations, and database instances, we obtain a function on instances that is the identity on r, namely

        h(r) = r.

I can understand 1), but I cannot understand 2).

In mathematics, an automorphism is a 1-1 mapping that preserves the structure of an underlying set. For example, if in some set whose members x, y and z obeys

        z = x + y,
then we expect an automorphism f on that set to also obey