I guess that’s one of the reasons I do write here, to trap in amber these states of emotion and experience in some way so I can look back and ultimately think that I was writing a lot more in [insert year here] even though I probably at that time felt I did a lot more writing in some other era of my life
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.
Haven't you seen Jurassic Park? :-)
Insects trapped in amber have been found dating back to the age of the dinosaurs. The point is that amber can preserve things extremely well dating back over millenia. See this article.
In the paragraph you wrote, the author is saying that they want to preserve their "states of emotion and experience" and not forget them.