Actually, a palindrome can be just about anything that is the same both forwards and backwards. (See http://en.wikipedia.org/wiki/Palindrome)
The Greeks and Romans had a type of palindrome in which the words rather than letters are read in reverse order. “Jack loves Jill, not Jane” versus “Jane, not Jill, loves Jack”. This is harder in English, so it never caught on. (The Mother Tongue: English and How it Got That Way by Bill Bryson, pages 229-230)
Could a palindrome be a sentence with the same meaning both forwards and backwards? That is considerably more difficult. “Are you as smart as I am?” is the best I can do.
And then there are mathemathical palindromes. Of course it’s not difficult to write palindromic number sequences, so how do recreational mathematicians make this a worthwhile challenge? One way is to investigate numbers squared. Squaring 11 is a pretty simple example — 121 — but some take it much farther. What’s the square of 2285? This came from a book with the improbably sounding title The Simpsons and Their Math Secrets by Simon Singh. (http://www.amazon.com/Simpsons-Their-Mathematical-Secrets-ebook/dp/B00CIR97UW/ref=sr_1_1?s=books&ie=UTF8&qid=1420902449&sr=1-1&keywords=math+simpsons)
If all this sounds a bit frightening, that’s covered too. Fear of palindromes is aibohphobia, which itself is a… okay, I’ll stop now.