What does a double helix in DNA is held together by?

First off - it is important to understand that a nucleotide (the monomer of DNA) is composed of 3 things: a sugar, a phosphate group, and a nitrogenous base. Next - understand that the "backbone" of DNA is composed of the sugars and phosphates.

That leaves you with nitrogenous bases. Hydrogen bonds form between the nitrogenous bases off opposite strands in the double helix. THIS is what holds the double helix together.