die Geschicklichkeit
dexterity
The ability to carry something out precisely, quickly, and skillfully, especially with the hands.
Ein Uhrmacher braucht eine ruhige Hand und große Geschicklichkeit.
A watchmaker needs a steady hand and great dexterity.

skill / dexterity
Loading your saved state.
dexterity
The ability to carry something out precisely, quickly, and skillfully, especially with the hands.
Ein Uhrmacher braucht eine ruhige Hand und große Geschicklichkeit.
A watchmaker needs a steady hand and great dexterity.

'Geschicklichkeit' (skill/dexterity) is the noun corresponding to the adjective 'geschickt' (skillful). The suffix '-keit' turns adjectives into nouns that describe a quality or ability.
Er ist sehr geschickt, deshalb bewundere ich seine Geschicklichkeit.
He is very skillful, which is why I admire his dexterity.
The context tells you whether manual or social ability is meant. If it is about hands, tools, or sports, manual ability is meant. With negotiations, conversations, or conflicts, social cleverness is meant.
Das Falten der kleinen Papierfiguren erfordert viel Geschicklichkeit.
Folding the small paper figures requires a lot of dexterity.
In connection with manual skills, the word is often used with verbs such as 'erfordern' (to require), 'beweisen' (to demonstrate), or 'trainieren' (to train). Typical adjectives are 'handwerklich' (craft/manual) or 'motorisch' (motor).
Ein Chirurg muss große Geschicklichkeit beweisen.
A surgeon must demonstrate great dexterity.
When it is about social competence, typical combinations are 'diplomatische Geschicklichkeit' (diplomatic skill) or 'taktische Geschicklichkeit' (tactical skill). You can master a situation 'mit Geschicklichkeit' (with skill).
Dank seiner diplomatischen Geschicklichkeit konnte ein Kompromiss gefunden werden.
Thanks to his diplomatic skill, a compromise was found.
art
'die Kunst' and 'die Geschicklichkeit' can both mean a special ability. 'Kunst' often sounds a bit bigger and emphasizes that something is difficult and requires a lot of practice or feeling. 'Geschicklichkeit' is more about someone doing something confidently, precisely, and cleverly, often with their hands or in a difficult situation. When you say 'Das ist eine Kunst' (that is an art), you often mean: not everyone can do that. 'Geschicklichkeit' fits better when describing a person’s practical skillfulness.

Mit viel Geschicklichkeit reparierte sie das kleine Uhrwerk.
With great dexterity, she repaired the small clockwork mechanism.
Die Kunst besteht darin, ruhig zu bleiben, wenn alle gleichzeitig etwas wollen.
The art lies in staying calm when everyone wants something at the same time.