The double helix structure of DNA is the result of two intertwined hydrogen bonds between the sugar-phosphate backbone and the bases. These hydrogen bonds are held together by chemical groups called bases. The bases are hydrophobic (water avoiding) and nonpolar (unlike water) to create a polar effect that enhances the attraction between them.
The base pairing in DNA stabilizes itself through hydrophobic forces, which is why it is so difficult to separate the two strands.