außergewöhnlich
exceptional
Impressive, positive, or remarkable to a very high degree; far above average.
Sie verfügt über ein außergewöhnliches Talent für das Klavierspiel.
She has an exceptional talent for playing the piano.

exceptional / unusual
Loading your saved state.
exceptional
Impressive, positive, or remarkable to a very high degree; far above average.
Sie verfügt über ein außergewöhnliches Talent für das Klavierspiel.
She has an exceptional talent for playing the piano.

The word is a clear compound of 'außer' (outside/beyond) and 'gewöhnlich' (ordinary/usual). So it literally means 'outside the ordinary' and is therefore easy to understand.
Das Museum zeigt eine Sammlung außergewöhnlicher Kunstwerke.
The museum is showing a collection of exceptional works of art.
'Außergewöhnlich' (exceptional/unusual) is very flexible. It can stand before a noun, serve as a description after a verb like 'sein' (to be), or function as an adverb to intensify a verb or adjective.
Er hat eine außergewöhnliche Begabung.
He has an exceptional gift.
In its positive meaning, 'außergewöhnlich' (exceptional) is often combined with nouns that express a special ability or quality. Typical examples are 'außergewöhnliches Talent' (exceptional talent), 'außergewöhnliche Leistung' (exceptional performance), or 'außergewöhnliche Schönheit' (exceptional beauty).
Der Sportler zeigte im Wettkampf eine außergewöhnliche Leistung.
The athlete delivered an exceptional performance in the competition.
especially / special
'besonders' and 'außergewöhnlich' both describe something that is not completely normal or that stands out strongly. 'besonders' is very flexible: it can simply mean 'very' or say that something is special. 'außergewöhnlich' is stronger and means that something clearly differs from what is usual. It can sound positive, for example with a very good performance, or neutral to strange when something is unusual. In everyday life, 'besonders' is often enough for smaller points of emphasis. 'außergewöhnlich' is used when something is clearly above average or truly unusual.

Das Konzert war außergewöhnlich, weil die Musiker im ganzen Raum gespielt haben.
The concert was unusual because the musicians played throughout the whole room.
Die Gäste haben sich besonders über die selbst gemachte Suppe gefreut.
The guests were especially happy about the homemade soup.