I assume they just want to express that a Pronominaladverb has itself a pronoun-like function, and in some cases, it replaces what would otherwise have been expressed as a pronoun that itself has replaced a noun.
Ich war voriges Jahr auf einem Konzert. Ich erinnere mich gut daran.
Theoretically, both of the following sentences are equivalent to the second one:
- Ich erinnere mich gut an es.
- Ich erinnere mich gut an das Konzert.
This is a transitive relation, somehow: an das Konzert ~> an es ~> daran. However, while all variants have the same denotation, the one repeating das Konzert sounds weird in this context, because it does not refer to already given information by a pronoun. (That is unidiomatic information structure.)
(Ich erinnere mich gut an es also sounds somewhat unidiomatic, but only because the daran form is blocking it; it's not "wrongly" information structured.)
There are other cases where the replacement is not appearent:
Ich erinnere mich gut daran, dass dort XYZ gespielt hat.
Here we could theoretically make up an elliptic an die Tatsache, dass, but this "hidden phrase" has conversational function, similar to an impersonal es, and is not directly referring to a previous piece of syntax, but to an implied conception of the context given indirectly by previous information. (Or alternatively, you can interpret it as a refererence to the following sentence dass dort XYZ gespielt hat, but that's also not simply a noun.)