
herunter
down
Expresses movement from a higher to a lower position; downward.
Er kletterte vorsichtig die Leiter herunter.
He carefully climbed down the ladder.
down
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down
Expresses movement from a higher to a lower position; downward.
Er kletterte vorsichtig die Leiter herunter.
He carefully climbed down the ladder.

down
Indicates a reduction or drop in a level, value, or condition.
Die Temperatur ist auf null Grad herunter gegangen.
The temperature has gone down to zero degrees.

downloaded
Colloquial for the completion of a download from the internet.
Ist das große Update schon herunter?
Is the big update downloaded already?

to be worn out
In a fixed expression: to be physically or emotionally exhausted, drained, or in a bad state.
Nach der langen Arbeitswoche bin ich mit den Nerven total herunter.
After the long workweek, my nerves are completely shot.
'Herunter' (down) consists of 'her' and 'unter'. The direction 'her' describes movement toward the speaker. So 'herunter' means 'down, toward me'.
Ich bin oben, wirf den Ball zu mir herunter!
I'm up here; throw the ball down to me!
'Herunter' (down) is a common prefix for separable verbs such as 'herunterladen' (to download), 'herunterfallen' (to fall down), or 'herunterkommen' (to come down). In a main clause, the prefix stands at the end.
Pass auf, dass die Tasse nicht vom Tisch herunterfällt.
Be careful that the cup doesn't fall down from the table.
The expression 'herunter sein' (to be worn out) or 'mit den Nerven herunter sein' (to be at the end of one's rope) is a fixed idiom. It means that someone is completely emotionally or physically exhausted.
Nach dem Marathon war ich körperlich total herunter.
After the marathon, I was physically completely worn out.
In colloquial speech, 'herunter' (downloaded) is often used without the verb 'laden' (to load/download) to express that a download is complete. The question 'Ist es schon herunter?' (Is it downloaded already?) is very common.
Das Spiel ist riesig, es wird Stunden dauern, bis es herunter ist.
The game is huge; it will take hours until it's downloaded.
down / downward
Herunter and hinunter both describe movement downward. Herunter is especially appropriate when something is moving toward the speaker or an important point of reference; hinunter emphasizes movement away from that point. So ask yourself whether the destination is with the speaker or farther away.

Bring bitte die Kiste vom Dachboden herunter.
Please bring the box down from the attic.
Die Wanderer gingen den steilen Weg zum Tal hinunter.
The hikers walked down the steep path to the valley.