A palindromic number is a number that remains the same when its digits are reversed. For example, the number 121 reads the same forwards and backwards, making it a palindromic number. This property can apply to any numerical base, but it is most commonly discussed in base ten. Palindromic numbers can be found in various ranges, from single-digit numbers like 7 to larger numbers like 12321. They are often used in recreational mathematics and can be interesting to explore due to their unique symmetrical properties.