I saw it in the zoo a few years back.
I also have the brain of an elephant.
It’s in a jar on my desk…
I’m not allowed back at the zoo…
…I feel dumb. I don’t get it.
There is an idea or saying that elephants never forget or that they have very good memories First article in google about this.
So to say you have a memory of an elephant could mean your memory is very good.
The twist is that this can also mean you remember seeing an elephant, which is what the second line implies.
[off topic?]
I haven’t heard the expression “an elephant never forgets” in quite a while. It’s funny how some expressions come and go. “Tight as the bark on a tree” for cheap and “boiled as an owl” for drunk are ones that I know, but haven’t used in conversation in years.