A palindromic sequence is a nucleic acid sequence in a double-stranded DNA or RNA molecule whereby reading in a certain direction (e.g. 5' to 3') on one strand is identical to the sequence in the same direction (e.g. 5' to 3') on the complementary strand. This definition of palindrome thus depends on complementary strands being palindromic of each other.
The meaning of palindrome in the context of genetics is slightly different from the definition used for words and sentences. Since a double helix is formed by two paired antiparallel strands of nucleotides that run in opposite directions, and the nucleotides always pair in the same way (adenine (A) with thymine (T) in DNA or uracil (U) in RNA; cytosine (C) with guanine (G)), a (single-stranded) nucleotide sequence is said to be a palindrome if it is equal to its reverse complement. For example, the DNA sequence ACCTAGGT is palindromic with its nucleotide-by-nucleotide complement TGGATCCA because reversing the order of the nucleotides in the complement gives the original sequence.