The answer is hydrogen bonds.
In the DNA double helix structure nitrogen atoms are chemically bonded to hydrogen atoms. Given that nitgrogen atoms are more electronegative than hydrogen atoms, hydrogen atoms in a base-pairing will bear a partial positive charge.
That partial positive charge is atracted to the oxygen atoms (which are also more electronegative than hydrogen atoms) in the same base pairing in DNA.
That atraction constitutes the hydrogen bond.
