What is the biological significance of finding palindromes in DNA sequence?
My knowledge of biology is extremely limited, but this is what I know of palindromic sequences:

Palindromic sequences are their own reverse complements. I have seen many restriction sites be palindromic. Also, some Transcription Factor Binding sites are palindromic. The canonical E-box site, for example, can be expressed as CANNTG.

Also, these palindromes, when occurring in pairs with a sequence between the occurrences, can double back and bind to each other (when the DNA is transcribed to RNA, say), and this would result in the RNA stem and loop structure.