Restriction enzymes (aka restriction endonucleases) recognize specific 4-8 bp double-stranded DNA sequences and cut the DNA backbone at a defined position within those sequences. The specific sequence where a restriction enzyme cuts is called a restriction site or cleavage site. Most cleavage sites are palindromes, meaning they are the same if read from either direction (like the word racecar or sequence GTATG).
When DNA has been processed with a restriction enzyme, it has been digested. If the restriction enzyme cuts each backbone at the same position, then the resulting DNA has blunt ends. If the restriction enzymes nicks each DNA backbone in a staggered manner, then there are single-stranded overhangs called sticky ends.
After restriction digestion, DNA fragments from different sources can be joined together using ligase. Sticky ends readily anneal, mean they quickly bind together with complementary sequences -- including other sticky ends. Since DNA strands are complementary, a restriction enzyme is identified only by its name, recognition sequence and the polarity of that sequence. For example, EcoRI nicks 5'-GAATTC-3'. A restriction map shows all the cleavage sites of a genome. A cleavage site is any location that can be nicked by a restriction enzyme.