Isolation and prominence are the two key criteria to classify a peak as an independent mountain.

To understand the meaning I like the visualization from the German Wiki page:

"Dominanz" is the german term for isolation. "Schartenhöhe" is the german term for prominence.

Isolation is the distance to the next point with the same height (radius) of a higher mountain. So the nearest higher mountain seen from B is A, see the distance marked as "Dominanz".

Prominence is the difference from the peak to the next key col to which you have to descend at least to be able to reach a higher peak. So from summit B you have to descend at least to the col between B-C, therefore the marked "Schartenhöhe". The col between B-B' is not relevant because B is the higher peak.

Isolation and prominence are the two key criteria to classify a peak as an independent mountain.

To understand the meaning I like the visualization from the German Wiki where

• "Dominanz" means isolation and
• "Schartenhöhe" means prominence:

Isolation is the distance to the next point with the same height (radius) of a higher mountain. So the nearest higher mountain seen from B is A, see the distance marked as "Dominanz".

Prominence is the difference from the peak to the next key col to which you have to descend at least to be able to reach a higher peak. So from summit B you have to descend at least to the col between B-C, therefore the marked "Schartenhöhe". The col between B-B' is not relevant because B is the higher peak.