It means that the surroundings of the atoms in a molecule are indistinguishable from one another. The surroundings of the atoms must be totally equivalent, they cannot simply be attached to the same type of atom, second and successive neighbours must also be exactly the same for both atoms, for them to be in equivalent environments.
The example you gave is correct (two D's attached to the same atom) but it is not the only case where atoms are in the same environment.
I have attached some examples, which I hope will make my explanation clearer.