They’re words or phrases that read the same backwards and forwards, like wow, huh, kayak, tenet, radar, level, racecar, boob, avid diva, air an aria, Tahitti hat, and Wassamassaw (a SC town).
Some names are palindromes, like Eve, Elle, Hannah, Mom, Dad, and Madam.
Making them up in phrases or whole sentences is a hobby that goes back to ancient Greece, and it can be fun. A well-known one is, “A man, a plan, a canal: Panama.” It’s amazing that people can keep coming up with so many of them. They’ve been involved in witchcraft and religious ritual. Back in the 50s there was a palindrome board game, and there’s even a 15-year-old magazine called The Palindromist, edited by Mark Saltveit, which traces the history of the pastime and includes interesting puzzlers, like calculator words, wherein you turn a calculator upside down and the numbers spell out words. (Maybe a neat code device for a spy novel?) There are also newspaper, magazine, and live competitions, some with cash prizes.
If you’d like to try palindroming, here’s a long list of clever ones to get you thinking in both directions: http://www.palindromelist.net
Myself, I don’t write palindromes. I write sagas.