die Eingangstür
front door
The door through which one enters a building, apartment, or room; the main entrance.
Bitte schließen Sie die Eingangstür, wenn Sie das Haus verlassen.
Please close the front door when you leave the house.

front door
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front door
The door through which one enters a building, apartment, or room; the main entrance.
Bitte schließen Sie die Eingangstür, wenn Sie das Haus verlassen.
Please close the front door when you leave the house.

This noun is made up of 'Eingang' (entrance) and 'Tür' (door). The linking element '-s-' connects the two parts. Literally, then, it is simply the door of the entrance.
Der Schlüssel für die Eingangstür hängt am Schlüsselbrett.
The key for the front door is hanging on the key rack.
The component 'Eingang' (entrance) is derived from the verb 'eingehen' (to go in/enter). If you recognize 'Eingang', you will also understand other words such as 'Eingangshalle' (entrance hall), 'Eingangsbereich' (entrance area), or 'Eingangsexamen' (entrance exam).
Im Eingangsbereich des Hotels wartete bereits ein Mitarbeiter auf uns.
An employee was already waiting for us in the entrance area of the hotel.
Common actions connected with the 'Eingangstür' (front door) are: 'an der Tür klingeln/klopfen' (to ring/knock at the door), 'die Tür aufschließen/abschließen' (to unlock/lock the door), or 'vor der Tür warten' (to wait in front of the door).
Der Postbote klingelte an der Eingangstür, aber niemand öffnete.
The mail carrier rang the front doorbell, but no one opened the door.
gate / goal
'das Tor' and 'die Eingangstür' can both be an entrance that you go through to get inside. The difference is in the size and the typical location. 'Eingangstür' is used for the door of a house, an apartment, or a room. 'Tor' is more suitable for large openings, for example in a wall, a fence, a garage, or a courtyard. Learners may confuse the words because both open access to a place. For a normal apartment, however, you almost always say 'Eingangstür', not 'Tor'.

Am Morgen steht ein Paket vor der Eingangstür.
In the morning, there is a package in front of the front door.
Das Tor zum Hof ist abends immer abgeschlossen.
The gate to the courtyard is always locked in the evening.