This is the 15056th most frequent Russian word.
позапрошлого
"Позапрошлого" means "the one before last" or "previous to the last."
Here, 'позапрошлого' is used in the genitive case as 'позапрошлом', modifying 'году'. It indicates a past year occurring prior to the last one.
В позапрошлом году я ездил в Москву.
The year before last, I went to Moscow.
In this sentence, 'позапрошлого' is used as a modifier of 'века', denoting a century before the last one.
Дело позапрошлого века всё ещё обсуждают историки.
The matter of two centuries ago is still discussed by historians.
Here, 'позапрошлое' is used in the accusative case as 'позапрошлое лето', referring to a summer that happened before the last summer.