1. Identify what stabilizes the double helix of DNA

   DNA consists of two polynucleotide strands wound around each other in a double helix. The two strands are held together mainly by hydrogen bonds between complementary nitrogenous bases:

   • Adenine pairs with Thymine through 2 hydrogen bonds
   • Guanine pairs with Cytosine through 3 hydrogen bonds

2. Check each option

   A: dipole-dipole interaction
   These are weaker intermolecular interactions and are not the principal reason for the specific double helical pairing of DNA strands. So, incorrect.

   B: hydrogen bonding
   This is the main interaction responsible for holding the two strands together through base pairing. So, correct.

   C: electrostatic attractions
   In fact, the phosphate groups in DNA backbone are negatively charged, so electrostatic attraction is not the main cause of helix formation between strands. So, incorrect.

   D: van der Waals' forces
   These may contribute slightly to stabilization, but they are not the primary reason typically asked in such questions. So, incorrect.

3. Conclusion

   The double helical structure of DNA is due to the operation of hydrogen bonding between complementary bases.

$\boxed{\text{B: hydrogen bonding}}$