der Augenblick
moment
A very short period of time; a moment.
Warten Sie bitte einen Augenblick, ich bin sofort für Sie da.
Please wait a moment, I'll be right with you.

moment
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moment
A very short period of time; a moment.
Warten Sie bitte einen Augenblick, ich bin sofort für Sie da.
Please wait a moment, I'll be right with you.

'Augenblick' (moment) is a compound of 'Auge' (eye) and 'Blick' (glance/look). So it literally describes the span of time that a brief glance takes—a very short moment.
Es dauerte nur einen Augenblick, bis das Licht wieder anging.
It only took a moment for the light to come back on.
The phrase 'Einen Augenblick, bitte!' (One moment, please!) is a very common and polite way to ask someone to wait briefly. It is often used as a standalone response.
„Haben Sie kurz Zeit?“ – „Einen Augenblick, bitte, ich telefoniere gerade.“
'Do you have a moment?' — 'One moment, please, I'm on the phone right now.'
Common phrases are 'im richtigen Augenblick' (at the right moment) or 'jeden Augenblick' (any moment now, shortly). The latter expresses an expectation.
Er kam im richtigen Augenblick, um uns zu helfen.
He came at the right moment to help us.
When 'Augenblick' (moment) describes a special, emotional moment, the preposition 'in' or the demonstrative article 'dieser' (this) is often used to emphasize the intensity of the moment.
In diesem Augenblick wusste sie, dass sie die richtige Entscheidung getroffen hatte.
At that moment, she knew that she had made the right decision.
minute
'die Minute' and 'der Augenblick' can both mean a short time. 'Minute' can also be an exact unit of time, namely sixty seconds. 'Augenblick' is not exactly measurable and sounds more like a very short moment. People often say 'einen Augenblick bitte' (one moment, please) when someone should wait briefly. 'Eine Minute bitte' (one minute, please) sounds a bit more specific and can also mean that it will take about a minute.

Einen Augenblick später klingelte das Telefon erneut.
A moment later, the phone rang again.
Nach zwei Minuten war die Gruppe wieder bereit für das Training.
After two minutes, the group was ready for training again.