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 it recognises palindromic sequence that is, sequences that are the same whether they are read forwards or backwards. These "sticky" ends allow the insertion of 'foreign' DNA into the host genome. By cutting the plasmid with the same restriction enzyme, the same 'sticky ends' are produced. For example, complementary bases of the plasmid can pair with those of the host DNA and form hydrogen bonds which anneal the two strands together. However, there will still be nicks in the phosphodiester bonds which form the rigid phosphate backbone of DNA. In this scenario DNA ligase can be added which will form the phosphodiester bonds between the recombinant strands. The genes carried on the plasmid will now be incorporated into the hosts genome.
Also see "blunt" ends.