I was doing an English exercise and I read the following sentence:
Ask Walter, he knows who's who.
Here, what is the meaning of "who's who"?
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It's an idiom. It means "He knows who each person is". It suggests that Walter knows the importance of the role of each person, not just their name.
He knows who is important and who is not important.
It is used as the name of a dictionary of important people, published each year since 1860.
You'll also hear "what's what" (what is important and what is not important)
As others said, it's an idiom meaning "knows who each person is". It can be understood this way:
Who's - an abbreviation for "who is". So the phrase expands to "they know who is who".
The thing is, that the word "who" can be used in several ways, signifying subtly different things.
We often use "who" colloquially, to mean "which person?" For example at a hospital, "Who's the doctor" (which of those people is the doctor), or "Who did this?" (which of these people is responsible). So the first "who" connotes that we are asking about which person, or people are .... something. (Who is....... [who])
But then what does the second "who" mean? It means some kind of identifier, their name, their role, their importance, their place, their job... some attribute that acts as an identifier for a person - literally "who they are" in the context.
This can be seen in everyday life. We often use "who" in this second sense, not meaning "which person/which of these people is (the doctor or whatever)" or "what is their name", but instead a third meaning, "I want to know relevant information about some person". This can be seen in this example: if someone bangs on the door at 3 am and we ask "Who are you?", we aren't really asking just their name, we really want to know their relevance or significance - if they are a police officer, a neighbour, a family member, a co-worker - some relevant information. If someone we don't know just said "I'm John McGuire" and nothing more, we would probably feel they were playing games or not answering the question, and we might ask more directly, "What do you want?" (What is the relevant information about you being here banging on my door at 3 am).
So the phrase overall has a sense that "they know which people have which (roles, significance, importance, names)" or whatever is relevant to the context.
In other words, like other answers say, "They know who each person is".
The same applies to "which is which", or "what is what". The structure is identical, and means roughly, "they know the (significance, purpose, function, name, importance) of each (item or thing referred to)".
"What a laboratory. All those chemicals! You really know which is which?" (which chemical has what name, significance, use - or in simple terms, the name/use/significance of each chemical)
Note that because "what" is such an open ended word, the phrase "she knows what's what" can also be used for the related meaning "she understands and can make sense of the things" (and probably, can do things about them if the context allows). For example:
"My car engine is broken, I don't have any idea what has happened!
"I'll call my mechanic. She will know what's what."
"This is a complicated project, do you need help?"
"No thank you I know what's what." (I understand/can make sense of the things, and I can know or work out what to.do)
"Fine, then I will let you get on with it."