hervorragend
excellent
Describes something of exceptionally high quality; excellent, outstanding.
Das Essen im neuen Restaurant war wirklich hervorragend.
The food at the new restaurant was truly excellent.

excellent / protruding
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excellent
Describes something of exceptionally high quality; excellent, outstanding.
Das Essen im neuen Restaurant war wirklich hervorragend.
The food at the new restaurant was truly excellent.

The word is the present participle of the verb 'hervorragen' (to stand out / protrude), which is made up of 'hervor' (out) and 'ragen' (to tower / rise). So it literally describes something that 'herausragt' (stands out) from a group—whether through its physical form or through its quality.
Sie hat eine hervorragende Leistung gezeigt und den Wettbewerb gewonnen.
She delivered an excellent performance and won the competition.
'Hervorragend' (excellent) can not only describe a noun (attributive) or be used with 'sein' (to be) (predicative), but also function as an adverb to modify a verb. It then means 'in an excellent way'.
Die Sängerin hat die Arie hervorragend interpretiert.
The singer interpreted the aria excellently.
In its main meaning, 'exzellent' (excellent), the word is often used to evaluate performances or results. Typical combinations are 'hervorragende Arbeit' (excellent work), 'eine hervorragende Idee' (an excellent idea), or 'ein hervorragendes Ergebnis' (an excellent result).
Für seine hervorragende Arbeit erhielt er eine Beförderung.
He received a promotion for his excellent work.
The literal meaning 'herausstehend' (protruding) is rare and is used almost only in geographical or anatomical descriptions. Words like 'Fels' (rock), 'Kinn' (chin), 'Knochen' (bone), or 'Punkt' (point) in the context point to this meaning.
Der Bergführer zeigte auf einen hervorragenden Felsen in der Wand.
The mountain guide pointed to a protruding rock in the wall.
good
'gut' and 'hervorragend' both describe a positive quality. 'gut' is normal and can be used broadly: for food, work, ideas, or performances. 'hervorragend' is stronger. It means not just good, but very good or especially good. That is why 'hervorragend' fits well when you want to give special praise to a performance, a result, or a quality. In everyday life, 'gut' is often enough. When something is clearly above the normal good level, 'hervorragend' is more precise.

Ihr Vortrag war hervorragend, weil alle Beispiele klar waren.
Her talk was excellent because all the examples were clear.
Nico hat den Termin gut vorbereitet.
Nico prepared the appointment well.