What does "donkey's years" mean — and why is it funny?

informal, British

Meaning

A very long time.

Where it comes from

A British phrase, probably a pun on 'donkey's ears', which are famously long — long ears quietly became long years.

Why it is funny

The humor is the hidden pun doing all the work. It sounds like a solemn measure of time, but it is really just a joke about a donkey's ears wearing a disguise.

Used in a sentence

"I haven't seen that film in donkey's years."