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Palindromes are relatively rare within the English language, the most famously quoted palindrome is 'madam' or 'did' is sometimes used as a very succinct way of demonstrating a palindrome.
The word is derived from the Greek word palindromes which means running back and forth again which sums up the whole effect of a palindrome.
Grammatically or used within the structure of language it is not regarded as being of any particular significance in the same way as an oxymoron or alliteration would be, it is just a quirk of language.