Restriction enzyme, a type of endonuclease, functions by "inspecting" the length of a $DNA$ sequence. Once it finds a recognition sequence, it binds and cut each of the two strands of the double helix at specific point leaving single stranded portions at the ends. This results in overhanging stretches called sticky ends. These are named so because they form hydrogen bonds with their complementary counter parts i.e., they can join similar complementary ends of $DNA$ fragment from some other source with the help of $DNA$ ligase. This stickness of the ends facilitates the action of the enzyme $DNA$ ligase, not $DNA$ polymerase.