Indicates that something happens after an interval of (X) years; used to mean 'for the first time in ... years'.
十年ぶりに故郷に帰ったら、町がずいぶん変わっていた。
When I returned to my hometown for the first time in ten years, the town had changed a lot.
彼女とは二年ぶりに連絡を取った。
I got in touch with her for the first time in two years.
大学のサッカー部は五年ぶりの優勝を果たした。
The university soccer club won the championship for the first time in five years.