Restriction enzymes are used to cut a large DNA strand into smaller segments. This is typically done to compare two people's DNA using gel electrophoresis, or to splice DNA from one organism into another. There are many different restriction enzymes that recognize different DNA sequences. For example, the restriction enzyme Aagl recognizes the DNA sequence...
You can view many restriction enzyme cutting sites at this wikipedia page. Notice that many of the recognized sequences are palindromes - the top strand is the reverse sequence of the bottom strand.
There are restriction enzymes that cut straight across the DNA leaving a 'blunt' end...
AatI - looks for
and cuts it like this
5' ---AGG CCT--- 3' 3' ---TCC GGA--- 5'
And there are restriction enzymes that cut the DNA but leave several nucleotides on one of the strands dangling off the end. This would be called a 'sticky' end because these single strand nucleotides will match up to their complementary nucleotides (if they are around) and connect into a double strand again.
Aaul - looks for
and cuts it like this...
5' ---T GTACA--- 3' 3' ---ACATG T--- 5'
Notice the catg nucleotides not matched up to anything. They will want to attach to other nucleotides and so will be considered 'sticky'.