
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.

by appearance
According to outward appearances; the way it looks at first glance.
Dem Augenschein nach war das Auto unbeschädigt, doch der Motor war kaputt.
By appearance, the car was undamaged, but the engine was broken.
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.
appearance
Allem Anschein nach expresses a supposition based on recognizable signs. Nach Augenschein describes a judgment based on how something looks on external inspection. The two can seem similar, but Augenschein places greater emphasis on visual examination.

Nach Augenschein ist das gebrauchte Fahrrad noch in gutem Zustand.
By appearance, the used bicycle is still in good condition.
Allem Anschein nach ist das gebrauchte Fahrrad noch in gutem Zustand.
Apparently, the used bicycle is still in good condition.