die Erscheinung
appearance
The outward appearance or form of a person or thing.
Mit seinem eleganten Anzug war er eine beeindruckende Erscheinung.
With his elegant suit, he was an impressive appearance.

appearance / phenomenon
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appearance
The outward appearance or form of a person or thing.
Mit seinem eleganten Anzug war er eine beeindruckende Erscheinung.
With his elegant suit, he was an impressive appearance.

'Die Erscheinung' is the noun related to the verb 'erscheinen' (to appear), which means 'to become visible' or 'to show up'. All meanings of the noun have to do with something that can be seen or perceived.
Plötzlich erschien eine Gestalt im Fenster.
Suddenly, a figure appeared in the window.
When 'Erscheinung' (appearance) describes a person's appearance, it is rather formal or literary. It describes the overall impression, not just the clothing. It is often combined with adjectives such as 'elegant', 'gepflegt' (well-groomed), or 'auffällig' (striking).
Sie achtet sehr auf eine gepflegte Erscheinung.
She pays a lot of attention to having a well-groomed appearance.
In scientific or natural contexts, 'Erscheinung' is often used for phenomena. It frequently forms compound words such as 'Naturerscheinung' (natural phenomenon), 'Randerscheinung' (marginal phenomenon), or 'Modeerscheinung' (fad).
Der Regenbogen ist eine optische Erscheinung in der Atmosphäre.
The rainbow is an optical phenomenon in the atmosphere.
This meaning is almost exclusively limited to media and publishing contexts. When it is about books, magazines, articles, or films, it means publication or release.
Wir feiern die Erscheinung der 100. Ausgabe unserer Zeitschrift.
We are celebrating the publication of the 100th issue of our magazine.
The meaning 'Geist' (ghost) or 'Vision' (vision) is often recognizable from adjectives such as 'geisterhaft' (ghostly), 'übernatürlich' (supernatural), or 'plötzlich' (sudden). The context is usually mysterious, religious, or eerie.
Im alten Schloss soll es nachts zu unheimlichen Erscheinungen kommen.
There are said to be eerie apparitions in the old castle at night.
spirit / mind
'der Geist' and 'die Erscheinung' can both occur in scary or supernatural situations. A 'Geist' is the being itself, usually the soul of a deceased person. An 'Erscheinung' is more the sudden becoming visible, or the visible figure. It can be a ghost, but as a word it mainly emphasizes the appearance. They can be confused because in stories people say that someone sees an 'Erscheinung' and may mean a ghost by that. In short: the 'Geist' is the being; the 'Erscheinung' is what you see.

Vor dem Fenster sah sie plötzlich eine dunkle Erscheinung.
In front of the window, she suddenly saw a dark apparition.
Die Kinder glauben, dass im Keller ein Geist wohnt.
The children believe that a ghost lives in the basement.