What is a restriction site?
That's the site in the DNA strand where the restriction enzyme makes a cut.
A palindrome is a sequence that is identical, forward and backward.
Think of the word "racecar" (read it backwards).
A restriction enzyme is an endonuclease that recognises a certain palindromic DNA sequence and makes a cut in the middle of it.
The first one discovered was EcoR1, extracted and purified from Escherichia Coli (E. Coli) by Frederic Sanger in the 1970's.
Its recognition sequence is CTTAAG. This doesn't look like a palindrome, until you realise that DNA is double-stranded:
When EcoR1 finds this sequence in dDNA (double-stranded DNA) it will make a cut between the A and the G-residues IN BOTH STRANDS. This results in "sticky ends" :
These sticky ends can then be joined ("glued") to other DNA-strands that are opened with the same restriction enzyme. The joining up is done by enzymes called Ligases.
That's how cloning started by the way....
After EcoR1, a whole multitude of other restriction enzymes were discovered, e.g. HinD3 (from Haemophilus Influenzae serotype 3(, SAu3A ( Staphylococcus Aureus ) etc.
Some have 6-positions recognition palindromic sites, others have a 4-base recognition sequence. The latter ones make more cuts in a given strand, as they will identify more occurrences of their cutting site.