in Principles and process of Biotechnology by

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A palindromic nucleotide sequence is the sequence of base pairs that reads the same both in forward as well as in backward direction. Palindromes are the base sequences that are read the same on the two stands but in opposite directions.

An example is:
5' GAATTC 3'
3' CTTAAG 5'

The sequence on one strand is GAATTC when read in 5' → 3' direction, the sequence on the opposite strand is CTTAAG read in 3' → 5' direction, but when both the strands are read in 5' → 3' direction the sequence is the base. Such a sequence is a Palindromic sequence.