noun, verbal noun, の adjective
You think about the concept of a certain number of times, each time thinking of each time you've thought about this concept before. Each time you look back, that is retrospection on that concept. You look back more and more times until there are no more times to look back on.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
I really like this retrospective scene in the movie.
Koichi was reminiscing incoherently with his cat on the veranda.
I know that Viet sometimes reminisces about his yakuza days during work hours.