A palindrome is a word, phrase, or sentence which can be read the same either forwards or backwards (punctuation, word spacing, and capitalisation are ignored for this purpose).
An easy example of a palindrome is the word “eye”, which can be read the same from either end.
Other examples of single words which are palindromes:
eve [the period immediately preceding an event; also Eve, the girl’s name]
otto [a variant of attar, an essential oil; also Otto, the boy’s name]
Some sentences or phrases which are palindromes:
Madam, I’m Adam
Madam, in Eden I’m Adam
Do geese see God?
Never odd or even
Murder for a jar of red rum
Was it Eliot’s toilet I saw?
Some men interpret nine memos
Are we not drawn onward, we few, drawn onward to new era?
Some humourous palindromes have been deliberately constructed as new words
aibohphobia = fear of palindromes [an ironic joke]
ailihphilia = love of palindromes
elihphile = lover of palindromes
Of interest are what are known as word squares, which can be read from left to right, as well as up and down; although these read as different words, not the same words, when read backwards. For example:
The palindromic Latin word square, “Sator Arepo Tenet Opera Rotas” (“The sower Arepo holds works wheels”), was found as a graffito at Herculaneum, buried by ash in 79 AD. This palindrome is remarkable for the fact that it also reproduces itself if one forms a word from the first letters, then the second letters, and so forth. Hence, it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left.
The Fortnightly Review, 15 January 1926, p.28 (bottom of right column)