noun
the hundredth year
Literal meaning: the 100th year of an era, period, or age. Often used in historical or chronological contexts.
この町は百年目を迎えた。
This town reached its hundredth year.
noun
end of one's rope; out of luck; rare chance; unusually good fortune
Idiomatic use derived from the idea of a once-in-a-century event. Sense 2 (out of luck) is often used in the phrase 百年目の不作 (a once-in-a-century bad harvest). Sense 3 (rare chance) is less common and may appear in expressions like 百年目の幸運 (once-in-a-century luck). Both are figurative and somewhat literary.
今年の不作は百年目だと言われている。
This year's poor harvest is said to be a once-in-a-century event.
こんな幸運は百年目だ。
Such good fortune is a once-in-a-century occurrence.
Compound of 百年 (hyakunen, 'one hundred years') + 目 (me, ordinal suffix). The literal meaning is 'the hundredth year'. The idiomatic senses likely developed from the notion of something happening only once in a hundred years, hence extremely rare, whether good or bad.