
schenken
to give
To give someone something as a gift without expecting anything in return.
Ich schenke meiner Mutter zum Geburtstag immer Blumen.
I always give my mother flowers for her birthday.
to give / pour
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to give
To give someone something as a gift without expecting anything in return.
Ich schenke meiner Mutter zum Geburtstag immer Blumen.
I always give my mother flowers for her birthday.

to skip
Colloquial for: to do without something; not to do something because it is unnecessary or too much effort.
Den Nachtisch können wir uns heute schenken, wir sind alle satt.
We can skip dessert today; we're all full.

to pour
To pour a drink, especially wine or beer, into a glass or cup.
Der Wirt schenkte uns noch eine Runde Bier ein.
The landlord poured us another round of beer.

to let slide
To waive or overlook something for someone, for example a penalty or a mistake.
Den kleinen Fehler im Test hat der Lehrer mir geschenkt.
The teacher let the small mistake in the test slide for me.
When you give someone something as a gift, the person receiving the gift is in the dative, and the thing being given is in the accusative. The pattern is: subject (nominative) + 'schenkt' + person (dative) + thing (accusative).
Er schenkt seiner Freundin einen Ring.
He gives his girlfriend a ring.
In the meaning 'auf etwas verzichten' (to do without something), 'schenken' (to skip) is used reflexively with the dative: 'sich etwas schenken'. It means that you do yourself the favor of not doing something.
Die lange Diskussion können wir uns schenken; wir sind uns ja einig.
We can skip the long discussion; we agree anyway.
The expression 'sich etwas schenken' in the sense of 'auf etwas verzichten' (to do without something) is colloquial. It is often used in everyday conversations.
Den Abwasch schenke ich mir heute und mache ihn morgen früh.
I'm skipping the dishes today and will do them tomorrow morning.
This meaning is used almost exclusively for pouring drinks, especially alcoholic ones like wine or beer, into a drinking vessel.
Kannst du mir bitte noch etwas Wasser schenken?
Can you please pour me some more water?
to give
Geben can also describe handing something over as a gift, but it does not always explicitly state that it is intended as a gift. Schenken clearly shows that the other person is meant to keep something without any expected compensation. When this intention is important, schenken is more precise.

Zum Geburtstag schenke ich meiner Schwester ein Buch.
I’m giving my sister a book for her birthday.
Zum Geburtstag gebe ich meiner Schwester ein Buch.
I’m giving my sister a book for her birthday.