A close variant is a version of your keyword that Amazon treats as effectively the same search — singulars and plurals, common misspellings, changes in word order, and stemmed forms. Close variant matching applies to exact match too, which is why an exact-match keyword still picks up search terms that are not literally identical to it, and why your Search Term report never lines up with your keyword list one for one.
Why exact match is not literal
Exact match means exact intent, not exact string. Amazon's reasoning is that 'water bottle' and 'water bottles' are the same shopper, and forcing advertisers to enumerate every spelling would produce worse matching.
The practical consequence is that you should read the search term column, not the keyword column, when judging what you actually bought.
Where it causes problems
Negation is the main one. A negative exact on a single spelling frequently leaves the variants running, which is why phrase-level negation is the reliable fix for a family of unwanted searches.
Harvesting is the other. Promote a term to exact and negate only that precise string in the discovery campaign, and the variants can keep serving there, competing with the exact campaign you just built.
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