der Halbmond
half moon
The appearance of the moon in which only a crescent-shaped half is visible from Earth.
Gestern Nacht stand ein schmaler Halbmond am Himmel.
Last night there was a narrow half moon in the sky.

crescent / half moon
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half moon
The appearance of the moon in which only a crescent-shaped half is visible from Earth.
Gestern Nacht stand ein schmaler Halbmond am Himmel.
Last night there was a narrow half moon in the sky.

The word is a clear compound of 'halb' (half) and 'der Mond' (the moon). It therefore literally describes a moon of which only half can be seen.
Bei klarem Himmel kann man den Halbmond gut erkennen.
When the sky is clear, you can see the half moon well.
You can recognize the meaning from the context: In connection with the sky, it refers to the moon. In texts about flags or religion, the symbol is meant. When the topic is food or baking, it refers to the pastry.
Der zunehmende Halbmond war am Abendhimmel sichtbar.
The waxing half moon was visible in the evening sky.
When referring to the pastry, 'Halbmond' (crescent pastry) is often combined with an ingredient to describe the filling or flavor. Typical examples are 'Nuss-Halbmond' (nut crescent), 'Mohn-Halbmond' (poppy-seed crescent), or 'Vanille-Halbmond' (vanilla crescent).
Diese Bäckerei ist für ihre leckeren Nuss-Halbmonde bekannt.
This bakery is known for its delicious nut crescents.
full moon
'der Vollmond' and 'der Halbmond' both describe how the moon looks in the sky. The difference is in the visible shape. With 'Vollmond', you see the moon as a whole round disk. With 'Halbmond', you see only a part of it in a crescent-like shape. Learners may confuse the words because both refer to phases of the moon and are built in a similar way. As a simple guide: 'voll' means round and fully visible, while 'halb' means only partly visible.

Heute Abend sieht man nur einen schmalen Halbmond am Himmel.
This evening, you can see only a narrow half moon in the sky.
Am Wochenende stand der Vollmond hell über dem See.
At the weekend, the full moon shone brightly over the lake.