A restriction enzyme can cut DNA at a specific sequence of nucleotides usually 4, 6 or 8 nucleotides long. This may result in symmetrical cleavage leading to "blunt" ends or assymetrical cleavage causing "sticky" ends. A "sticky" end is produced when the restriction enzyme cuts at one end of the sequence, between two bases on the same strand, then cuts on the opposite end of the complementary strand. This will produce two ends of DNA that will have some nucleotides without any complementary bases. A restriction enzyme will only cut at a specific sequence, and since DNA is palindromic the end of one sequence is the same as the opposite end of the complementary sequence. These "sticky" ends allow the insertion of 'foreign' DNA into the host genome. By using the same restriciton enzyme to cut a plasmid, for example, complementary bases of the plasmid can pair with those of the host DNA. The genes carried on the plasmid will now be incorporated into the hosts genome.
Also see "blunt" ends.