If the recognition site is cut in a staggered fashion by a restrictionendonuclease, the cut ends of the DNA double strand is left with a single strand which is a few nucleotide bases long.
If the same restriction endonuclease is used to cut DNA, then all the fragments produced will have ends that are complementary to each other. This means that the single-stranded end of any one fragment can be stuck to the single-stranded end of any other fragment (stickyends).
Once the complementary bases of two stickyends have paired up, an enzyme (DNA ligase) is used to bind the phosphate-sugar framework of two sections of DNA.
Stickyends have considerable importance because, provided that the same restriction endonuclease is used, they allow recombinant DNA to be formed from the DNA of different organisms.