The palindromes in DNA are base pair sequences that are the same when read forward (left to right) or backward (right to left) from a central axis of symmetry. The following sequence reads the same on the two strands in 5' —> 3' direction. This is also true when we read in the 3' —> 5' direction.
Restriction endonuclease enzymes recognize palindromic sequences in DNA and cut them.