What does "to trap in amber" mean and where does it come from?
Solution 1:
Apart from the aspect of preservation described by the other answers, another aspect occurs to me -- that is the ability of amber to preserve and by virtue of its relative transparency, still allow inspection.
I feel this would apply to the emotions mentioned in the question. It would still be possible to look back (in the words of the quote) through the 'amber' and access the emotions.
Solution 2:
It means to preserve for perpetuity, or at least, a very long time. Some creatures trapped in amber have been preserved for millions of years.
