When restriction enzymes jaggedly cut double stranded DNA it results in so called sticky ends. What is the substance that makes the DNA sticky?
The sticky ends are sticky because they have complementary bases. Typically used restriction enzymes cut the two complementary DNA strands at different spots, generating 'overhang', or sticky ends:
These overhangs allow for perfect base pairing (C with G, A with T), which is the result of hydrogen bonding. Just like water molecules show strong affinity to each other or other molecules with -OH and -H groups (e.g., alcohol), hydrogen bonds between nucleotides glues the ends together.
The principles of base-pairing has been nicely answered by @MadScientist in "Why does A pair with T and G with C?"
What are sticky ends. There is no substance that is attached making the DNA ends "sticky". What has actually happened is an overhang of at least a few nucleotides. Blunt ends are another kind of cut, but have no overhanging residues.
Why are sticky ends sticky? Restriction enzymes usually cut these ends deliberately so that a four nucleotides are overhanging on the 5' end of the double strand. These are complementary to other overhangs and because they are less stable than a bound double strand region, and are able to hydrogen bond easily with complementary bases, they are easier to attach with a ligase.
Below is an image of the base pairs interacting via H bonds.
The "substance" is hydrogen bonds (H-bonds), or rather the potential to form them. Each of the unpaired A/T bases in the sticky ends have the potential to form 2 H-bonds with a complementary T/A, and each of the unpaired G/C bases have the potential to form 3 H-bonds with a complementary C/G.
From the perspective of a biophysicist, H-bonds are often thought of as being the strongest intermolecular interactions. I personally think that it's a little bit lazy and unphysical to see things this way, but the prevailing view in the field is that H-bonds determine specificity in all macromolecular interactions (e.g. the specificity that causes a single DNA strand to bind mostly to complementary DNA strands and poorly to random DNA strands).