Used mainly in casual conversations among friends or family, not in formal situations. I haven't seen you in donkey's years! How have you been?
Pro Tip 2/3
British Origin
Primarily a British expression, understood in the UK but may confuse people from other countries. He's been with the company for donkey's years, since the very beginning.
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Exaggeration
It's an exaggeration, it doesn't mean a specific number of years, it just feels like a really long time. I've been doing this job for donkey's years, but it never gets easier.