How does the meaning of "Close the door." come from "Tür zu."?
I get that Tür means door. But how does zu mean close? I thought zu means to or too, and I can't fathom what I'm not understanding.
The translated phrase would be something like "Schließ die Tür!" or "Mach die Tür zu!". "Tür zu!" is colloquial, and extremely impolite.
Zu does indeed have quite a few meanings, like towards, at, too, or closed.
Some examples of its usage:
"Die Tür ist zu." - "The door is closed."
"Ich bin zu Hause." -"I'm at home."
"Das ist zu viel!" - "That's too much!"
"Lasst uns zu ihr gehen." - "Let's go to her."
The sentence is an ellipsis. As a complete sentence, it would be:
Mach die Tür zu!
The verb is zumachen ("close"). Tür zu! is used as a very short order, and is usually impolite and used to express anger.
The word »zu« has at least nine different meanings:
Preposition, to describe a movement towards a target:
Michael ging zu seinem Bruder.
Michael went to his brother.
In combination with an article:
Tom lief zum Auto. (... zu dem ...)
Tom ran to the car.
Tom lief zur Schule. (... zu der ...)
Tom ran to the school.
Preposition, to describe a relation:
Milch besteht zu einem großen Teil aus Wasser.
Milk consists to a large extent of water.
(You can also have articles joined with »to« as shown above)
Preposition, to describe that something happened at a certain time:
Ich werde dich zu Ostern besuchen.
I'll visit you at Easter.
(Joined articles are possible here too)
Adverb (most frequent usage in the phrase »ab und zu« which means »now and then« or »occasionally«)
Markus isst ab und zu Pizza.
Markus occasionally eats pizza.
Grade Particle (I'm not sure if this term is correct. In German it is a »Gradparticle«):
Dieser Mantel ist mir zu groß.
This suit is too big for me.
Konjunktion, together with um, ohne or anstatt as part of an infinite group.
Adrian fuhr ins Dorf, um Milch zu kaufen.
Adrian drove to the village to buy milk.
Dr. Weber arbeitete 60 Stunden durch, ohne zu schlafen.
Dr. Weber kept working for 60 hours without sleeping.
Die Kinder spielten, anstatt zu schlafen.
The children were playing instead of sleeping.
Adverb, to describe, that an action ends in a drunk or stoned state:
Kevin hat sich zu gekifft.
Kevin smoked pot until he was stoned.
Adverb, to describe, that an action ends in a closed state:
Walter macht die Tür zu.
Walter closes the door.
Adjektive, to describe, that something is closed.
Die Tür ist zu.
The door is closed.
Überall sieht man nur noch zue Türen. (Bad style, but colloquial speech in some regions)
You only see closed doors everywhere.
Your example is a variation of meaning 8 (Adverb to describe an action that ends in a closed state). »Tür zu« is a common ellipsis of this command:
Mach die Tür zu!