It's the Present Simple Passive.

i = subject am= "to be" conjugated for the subject "I" and used as a linking verb reminded= an adjective formed from the verb "to remind" of a time= part of prepositional phrase describing what "I" was reminded of.

It is not used often in conversation, it's a fancier choice of words. I can't imagine anyone saying it unless they were giving a presentation In a normal conversation, they would just say, "This/that reminds me of the time..."

Thank you all of you!