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](https://de.wikipedia.org/wiki/Dominanz_%28Geographie%29):

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/krWur.jpg

"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.