Prepositions connect words and groups of words together. They express the relation between living beings, things or contexts. Verbs with fixed prepositions, however, connect the verb with an object. So in this case, the prepositions don't provide a context for time or location but instead are used idiomatically with the verb. Sometimes they can even change the meaning of the verb.

Adverbs with "da(r)" + preposition
The object connected to a verb by a fixed preposition can be replaced by certain adverbs known as prepositional adverbs.

"da" + preposition or "dar" + preposition (when the preposition begins with a vowel) can be used when:

... the object or context was just mentioned and is therefore known.

Example:
Ich träume von einer eigenen Familie, Kinder, Haus, Hund!
Davon träume ich, Harry!
(= Julia has already told Harry about her dreams. That's why she can sum it all up in her second sentence.)

... when the object or context is explained immediately afterward.

Example:
Ich denke über etwas nach. — Worüber denkst du nach?
Ich denke darüber nach, dass ich mit Julia sprechen muss.

More:

"da(r)" + preposition can only be used for things, facts or circumstances. For living beings you have to use personal pronouns.

Example:
Ich träume von Julia – Ich träume von ihr.
Ich denke über Julia nach. – Ich denke über sie nach.