schärfen
to sharpen
To make an object, especially a blade, pointed or able to cut.
Der Koch muss vor der Arbeit seine Messer schärfen.
The cook has to sharpen his knives before work.

to sharpen
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to sharpen
To make an object, especially a blade, pointed or able to cut.
Der Koch muss vor der Arbeit seine Messer schärfen.
The cook has to sharpen his knives before work.

The verb 'schärfen' (to sharpen) is derived directly from the adjective 'scharf' (sharp). It literally means to make something sharp. This logic applies to all meanings: a knife, the mind, a law, or an image.
Diese Übung soll deine Beobachtungsgabe schärfen.
This exercise is meant to sharpen your powers of observation.
'Schärfen' (to sharpen) is a transitive verb and almost always requires an accusative object. So you almost always have to say what is being sharpened.
Der Redner versuchte, das Bewusstsein für das Problem zu schärfen.
The speaker tried to raise awareness of the problem.
You can always recognize the exact meaning of 'schärfen' (to sharpen) from the object: a knife is made able to cut, one's view becomes more attentive, and a law becomes stricter.
Man kann eine Soße mit Chili schärfen.
You can spice up a sauce with chili.
In its figurative meaning, 'schärfen' (to sharpen) is often used with mental or perceptual abilities. Typical phrases are 'den Blick schärfen' (to sharpen one's view), 'die Sinne schärfen' (to sharpen the senses), or 'das Profil schärfen' (to sharpen one's profile).
Ein Auslandsjahr kann den Blick für die eigene Kultur schärfen.
A year abroad can sharpen your view of your own culture.
This meaning of 'schärfen' (to sharpen/focus) belongs to the technical language of photography and image editing. It is used when talking about cameras, lenses, or software.
In der Nachbearbeitung kannst du das Bild noch etwas schärfen.
In post-processing, you can sharpen the image a little more.
to subtract / peel off
'abziehen' and 'schärfen' can both have to do with a blade that should cut better again. 'schärfen' is the more general word: you make a knife, scissors, or another blade sharp. 'abziehen' is more precise and means a specific kind of sharpening, usually with a honing steel or whetstone. In everyday language, people often simply say 'ein Messer schärfen' (to sharpen a knife). 'Ein Messer abziehen' (to hone a knife) sounds more precise when you mean the technique.

Der Mitarbeiter schärft die Messer, weil sie nicht mehr gut schneiden.
The employee sharpens the knives because they no longer cut well.
Vor dem Kochen zieht der Koch das Messer kurz am Wetzstahl ab.
Before cooking, the chef briefly hones the knife on the honing steel.