der Vortag
previous day
The day immediately before a specific, named day.
Am Vortag seiner Prüfung war er sehr nervös und konnte kaum schlafen.
On the previous day of his exam, he was very nervous and could hardly sleep.

previous day
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previous day
The day immediately before a specific, named day.
Am Vortag seiner Prüfung war er sehr nervös und konnte kaum schlafen.
On the previous day of his exam, he was very nervous and could hardly sleep.

The word is made up of the preposition 'vor' (before) and the noun 'Tag' (day). So it literally refers to the day 'before' a specific event.
Die Vorbereitungen für die Feier liefen schon am Vortag auf Hochtouren.
Preparations for the celebration were already in full swing on the previous day.
In most cases, 'Vortag' (previous day) is used in the fixed phrase 'am Vortag' (on the previous day) to indicate a point in time.
Am Vortag der Abreise hat sie noch schnell die Koffer gepackt.
On the day before departure, she quickly packed the suitcases.
'Vortag' (previous day) is a relative word. It always means the day before a specific date or event mentioned in the context, not simply 'yesterday'.
Die Konferenz begann am Mittwoch. Am Vortag gab es bereits ein informelles Treffen.
The conference began on Wednesday. On the previous day, there had already been an informal meeting.
yesterday
'gestern' and 'der Vortag' can both mean the day before another day. 'gestern' always depends on today's date: it is the day before today. 'der Vortag' depends on a named day or event: it is the day before that. This can be yesterday, but it does not have to be. Learners may confuse the words because both express 'the day before'. In everyday language, people usually say 'gestern'. 'Der Vortag' sounds more precise and fits well when talking about appointments, trips, exams, or reports.

Der Vortag der Prüfung war für Lisa sehr ruhig, weil sie schon alles gelernt hatte.
The day before the exam was very quiet for Lisa because she had already studied everything.
Gestern war der Verkäufer mit seiner Familie im Park.
Yesterday the salesman was in the park with his family.