etwas in Augenschein nehmen
to inspect
To look at, examine, or inspect something closely in order to form a personal impression of it.
Der Gutachter kam, um den Wasserschaden in Augenschein zu nehmen.
The expert came to inspect the water damage.

inspection / appearance
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to inspect
To look at, examine, or inspect something closely in order to form a personal impression of it.
Der Gutachter kam, um den Wasserschaden in Augenschein zu nehmen.
The expert came to inspect the water damage.

The word consists of 'Auge' (eye) and 'Schein' (appearance, in the sense of 'Anschein'). Literally, then, it means what appears to the eye. This explains its use in the context of visual inspection and first impressions.
Der erste Augenschein kann manchmal täuschen.
First appearances can sometimes be deceptive.
'Augenschein' is almost never used on its own. It is found almost exclusively in the fixed expressions 'etwas in Augenschein nehmen' (to inspect something) and 'nach/dem Augenschein' (by appearance).
Der Polizist nahm den Unfallort in Augenschein.
The police officer inspected the scene of the accident.
Expressions with 'Augenschein' belong to a more formal, often official or written style. In everyday language, you would more likely say 'sich etwas ansehen' (to look at something) or 'etwas prüfen' (to check something).
Der Architekt wird den Baufortschritt morgen in Augenschein nehmen.
The architect will inspect the construction progress tomorrow.
In the expression 'etwas in Augenschein nehmen' (to inspect something), 'etwas' is the accusative object. It refers to the thing that is being inspected closely.
Der Käufer wollte das gebrauchte Auto vor dem Kauf selbst in Augenschein nehmen.
The buyer wanted to inspect the used car himself before buying it.
impression
'Eindruck' and 'Augenschein' both have to do with what you perceive about something. 'Eindruck' more often means the feeling, effect, or assumption that arises. This can happen after a conversation, a visit, or an observation. 'Augenschein' is more strongly connected to seeing and checking something with your own eyes. People often say 'etwas in Augenschein nehmen' (to inspect something) when they look at something closely. The words can be confused because both lead to a personal assessment. In practice: 'der Eindruck' is the result in your mind, while 'der Augenschein' is more the close looking or outward appearance.

Vor dem Kauf nahm Herr Demir das Fahrrad genau in Augenschein.
Before buying it, Mr. Demir inspected the bicycle carefully.
Nach dem Gespräch hatte sie den Eindruck, dass der Arzt ihr gut zugehört hatte.
After the conversation, she had the impression that the doctor had listened to her carefully.