The phosphate groups in DNA are related to phosphoric acid, shown here with the phosphorus atom in purple or pink. The phosphorus atom is surrounded by four oxygen atoms, showm in red or orange.
Three of the oxygens in phosphoric acid bear hydrogen atoms. In DNA, two of these hydrogens can be replaced by the ribose goups from nucleotides, forming sugar phosphates.
The hydrogens separate readily from their oxygen atoms as hydrogen ions, H+. Sources of H+ ions are called acids, hence the name "phosphoric acid."