Things fuse, people do not
In English the pronoun simply slots in behind the preposition: I'm waiting for the bus becomes I'm waiting for it. German blocks that move. You cannot say auf es, mit es or über es. Instead the preposition fuses with da- and becomes one word: darauf, damit, darüber. This only works for things and ideas. For people the preposition keeps an ordinary pronoun.
Thing or person
Ich warte auf den Bus.
I'm waiting for the bus.
Ich warte darauf.
I'm waiting for it.
the bus is a thing, so the preposition fuses
Ich warte auf Anna.
I'm waiting for Anna.
Ich warte auf sie.
I'm waiting for her.
Anna is a person, so the pronoun stays separate
The r in the middle, and questions
If the preposition starts with a vowel, an r slides in between so the two parts do not collide: darauf, daran, darüber, worauf, worin. If it starts with a consonant, nothing is added: damit, davon, dafür, dazu, womit, wofür. The same pattern works for questions with wo-.
With and without r
Ich freue mich darauf.
I'm looking forward to it.
vowel: r inserted
Wir sprechen morgen darüber.
We'll talk about it tomorrow.
vowel: r inserted
Was hältst du davon?
What do you think of it?
consonant: no r
Questions with wo(r)- and wen/wem
Worauf wartest du?
What are you waiting for?
Auf wen wartest du?
Who are you waiting for?
Worum geht es?
What's it about?
Womit kann ich Ihnen helfen?
What can I help you with?
A placeholder for dass and zu clauses
A preposition cannot sit in front of a whole clause: Ich freue mich auf, dass du kommst is impossible. German puts the da- word in the main clause as a placeholder, and the clause that follows says what it stands for. With most verbs that take a preposition, the placeholder is required.
Placeholder, then clause
After the placeholder you can use a dass clause, a clause with ob or a W-word, or a zu-infinitive when both halves have the same subject.
Ich freue mich darauf, dich wiederzusehen.
I'm looking forward to seeing you again.
Denk bitte daran, dass wir morgen früh los müssen.
Please remember that we have to leave early tomorrow.
Es hängt davon ab, wie das Wetter wird.
It depends on what the weather is like.
Pointing back at what was just said
The da- words are not limited to verbs with a fixed preposition. Any preposition can fuse with da- to point back at a thing or a situation you have just mentioned. The beat falls on the second part: daMIT, daFÜR, daNACH.
Das ist mein neues Handy. Damit mache ich alle Fotos.
That's my new phone. I take all my photos with it.
Wir gehen erst essen. Danach können wir ins Kino gehen.
We'll eat first. Afterwards we can go to the cinema.
Dafür habe ich leider keine Zeit.
I'm afraid I haven't got time for that.
