This is an idiom that means you’re frustrated or mentally exhausted about something. It depends on the usage of “wit” being understood in its classical definition of “to be able to know or think,” which is listed in most etymologies as an “archaic” term from Old English.
So, to be at “your wit’s end” is to be running out of intelligence or the ability to reason about a situation.
The same definition applies to the phrase, “I survived on my wits alone.”
We tend to consider “wit” as being able to express yourself cleverly. That definition of “wit” dates from the 1500s.
Why I Looked It Up
I can’t remember, honestly. I knew the phrase, clearly, but wasn’t sure of the origin.
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