By "do" he means the behaviour of the objects, not their use in real-world applications. In general, you consider a bunch of isomorphic things as one, rather than worrying about the differences between them which have no effect on their behaviour. This is sort of handwavy because it depends on context.
For example, if we are considering sets and functions between them, we generally don't care about the exact names of the elements of the set, only the fact that they are distinct elements. The important aspects of a function in this case are properties such as injectivity, surjectivity, etc, not that it sends one particular element of one set to another particular element of another set.
Another example is in linear algebra: we really care about linear transformations on an abstract vector space more than we care about what that linear transformation looks like relative to a specific set of coordinates.
This point of view is espoused in category theory, where the important information is carried in the morphisms between objects, not really the objects themselves.
For example, if we are considering sets and functions between them, we generally don't care about the exact names of the elements of the set, only the fact that they are distinct elements. The important aspects of a function in this case are properties such as injectivity, surjectivity, etc, not that it sends one particular element of one set to another particular element of another set.
Another example is in linear algebra: we really care about linear transformations on an abstract vector space more than we care about what that linear transformation looks like relative to a specific set of coordinates.
This point of view is espoused in category theory, where the important information is carried in the morphisms between objects, not really the objects themselves.