die Umarmung
hug
The action of putting your arms around someone to express affection, comfort, joy, or a greeting.
Zur Begrüßung gab sie ihm eine herzliche Umarmung.
As a greeting, she gave him a warm hug.

hug
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hug
The action of putting your arms around someone to express affection, comfort, joy, or a greeting.
Zur Begrüßung gab sie ihm eine herzliche Umarmung.
As a greeting, she gave him a warm hug.

'Die Umarmung' (the hug) is the noun form of the verb 'umarmen' (to hug). The verb itself is made up of the prefix 'um-' and 'Arm' (arm) and literally means to put your arms around someone.
Er umarmte seine Mutter zum Abschied.
He hugged his mother goodbye.
'Umarmung' (hug) is very often combined with the verb 'geben' (to give). The person receiving the hug is in the dative: 'jemandem eine Umarmung geben' (to give someone a hug).
Er gab seinem Freund zur Begrüßung eine feste Umarmung.
He gave his friend a firm hug as a greeting.
To describe a hug more specifically, adjectives such as 'herzlich' (warm), 'fest' (firm), 'lang' (long), 'kurz' (short), or 'brüderlich' (brotherly) are often used.
Nach der langen Reise gab es eine lange und herzliche Umarmung.
After the long journey, there was a long and warm hug.
tenderness
'die Umarmung' and 'die Zärtlichkeit' can both express loving closeness. However, 'Umarmung' refers to a specific action: you put your arms around someone. 'Zärtlichkeit' is more general. It can be a feeling or a gentle, loving action, for example a touch or also a hug. So every loving hug can be a form of 'Zärtlichkeit', but not every 'Zärtlichkeit' is a hug. If you specifically mean the action with the arms, 'Umarmung' is clearer.

Vor der Reise gibt Jan seiner Mutter eine lange Umarmung.
Before the trip, Jan gives his mother a long hug.
Nach dem Essen zeigt sie ihre Zärtlichkeit mit einer sanften Berührung.
After dinner, she shows her tenderness with a gentle touch.