
vorziehen
to prefer
To like or prefer something or someone more than another person or thing.
Ich ziehe Tee dem Kaffee vor.
I prefer tea to coffee.
to prefer / move up / draw
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to prefer
To like or prefer something or someone more than another person or thing.
Ich ziehe Tee dem Kaffee vor.
I prefer tea to coffee.

to move up
To move an appointment or event to an earlier time.
Können wir das Treffen auf Montag vorziehen?
Can we move the meeting up to Monday?

to draw
To physically pull something forward, especially a curtain or drape, in order to cover a window.
Bitte zieh die Vorhänge vor, die Sonne blendet.
Please draw the curtains; the sun is glaring.

to start indoors
To grow young plants, usually from seeds, in a protected place, such as on a windowsill, before they are planted outdoors.
Im Februar beginne ich damit, Tomaten für den Garten vorzuziehen.
In February, I start growing tomatoes indoors for the garden.
'Vorziehen' (to prefer / move up / draw) is a separable verb with the prefix 'vor-'. In a main clause, the prefix comes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich ziehe einen ruhigen Abend zu Hause vor.
I prefer a quiet evening at home.
When expressing a preference, 'vorziehen' (to prefer) has a fixed structure: You prefer [something in the accusative] to [something else in the dative]. The thing you like more is in the accusative.
Er zieht das Landleben der Stadt vor.
He prefers country life to the city.
In the meaning 'to move something to an earlier time', the verb is often combined with time-related nouns such as 'Termin' (appointment), 'Treffen' (meeting), 'Besprechung' (meeting/discussion), or 'Reise' (trip).
Wir haben unseren Urlaub um eine Woche vorgezogen.
We moved our vacation up by one week.
The literal meaning 'to pull forward' is used almost exclusively in connection with curtains or drapes, in order to cover a window.
Es wird dunkel, du kannst schon mal die Vorhänge vorziehen.
It's getting dark; you can go ahead and draw the curtains.
This meaning is a technical term from gardening. It is used for plants, herbs, or vegetables that you grow indoors from seeds before planting them outside.
Ich ziehe meine Tomaten jedes Jahr auf der Fensterbank vor.
I start my tomatoes indoors on the windowsill every year.
to postpone / move / fence
Both verbs refer to changing the time of an appointment. According to the meanings given here, „Verschieben“ moves the appointment to a later time. „Vorziehen“ explicitly moves it to an earlier time. The direction of the change therefore determines which word to use.

Wir ziehen die Sitzung von Donnerstag auf Dienstag vor.
We are moving the meeting up from Thursday to Tuesday.
Wir verschieben die Sitzung von Dienstag auf Donnerstag.
We are postponing the meeting from Tuesday to Thursday.