elegant
Describes a person, clothing, or movement that is tasteful, graceful, and stylish.
Sie trug ein sehr elegantes Abendkleid.
She wore a very elegant evening gown.

Loading your saved state.
Describes a person, clothing, or movement that is tasteful, graceful, and stylish.
Sie trug ein sehr elegantes Abendkleid.
She wore a very elegant evening gown.

The meaning of 'elegant' depends strongly on the noun. If it refers to people, clothing, or movements, it means 'stilvoll' (stylish). If it refers to ideas, solutions, or methods, it means 'klug und einfach' (clever and simple).
Die Tänzerin war für ihre eleganten Bewegungen bekannt.
The dancer was known for her elegant movements.
In connection with appearance and style, 'elegant' is often combined with clothing, manner, or movements. Typical combinations are 'elegant gekleidet sein' (to be elegantly dressed), 'ein elegantes Auto' (an elegant car), or 'elegant aussehen' (to look elegant).
Er kam in einem eleganten Anzug zur Preisverleihung.
He came to the awards ceremony in an elegant suit.
In the abstract meaning, 'elegant' is often used in academic or technical contexts. Common combinations are 'eine elegante Lösung' (an elegant solution), 'eine elegante Methode' (an elegant method), or 'eleganter Code' (elegant code).
Die Ingenieurin entwickelte eine elegante Methode, um Energie zu sparen.
The engineer developed an elegant method for saving energy.
fine
'fein' and 'elegant' can both describe something beautiful, stylish, or high-quality. 'elegant' is especially suitable for clothing, people, or movements when something appears tasteful and stylish. 'fein' is broader: it can also refer to quality, delicate workmanship, or a refined impression, for example with fabric, food, or material. When style and appearance are the main focus, 'elegant' sounds more precise. When it is about quality or delicacy, 'fein' is often a better fit.

Bei der Feier trug Maria ein elegantes schwarzes Kleid.
At the celebration, Maria wore an elegant black dress.
Sie kaufte einen feinen Schal aus weicher Wolle.
She bought a fine scarf made of soft wool.