A ternary acid is a hydroxyl compound of non-metal oxides. Translated, ternary acids contain three kinds of atoms; a compound between a non-metal and an oxygen, and a hydroxide covalently bonded. If you're familiar with the definition of an acid, this should start to raise an alarm bell. Acids are very closely associated with hydrogen ions, whereas bases are equally associated with hydroxide ions. So why are these compounds with hydroxyl groups considered acids? According to the Arrhenius Theory first posited on the nature of acids and bases, they should not be, but this is in fact incorrect. Ternary acids are acids, despite appearences, and their nature can be explained through polar interactions.

As an illustraton, here is a standard ternary acid, nitric acid (HNO3):

   :O:
    ||
    N
   / \
 :O   O:
  "   "\
        H
You have your nitrogen-dioxide compound, a non-metal oxide, and you have your hydroxyl group. Take a look at the lone pairs dotting the oxygens. These represent unshared electrons, free-flying balls of negative charge not being used up in any bonds. Notice that there are two times as many of these on the non-metal oxide side of the molecule as on the hydroxyl. This is going to exert an effect. The high electronegativity of the free oxygens pull the nitrogen closer to them, strengthening the bond. To remain at an equilibreum of charge, oxygen must compensate by itself drawing closer to the nitrogen. All that's left is the hydrogen, which hangs out high and dry with a weakened bond from all the tugging. This type of interaction is called a dipole, and it's common with oxygen-heavy molecules. The hydroxyl bond is weak enough that the hydrogen atom is more likely to be plucked away by a hungry base than the hydroxide ion as a single unit. And according to the most recent Brønsted-Lowry Theory, any molecule that shares a hydrogen is an acid.

Ternary acids have their own special naming convention that indicate strength. The more oxygens one has in the molecule, the weaker the hydroxyl bond will be, the more likely the molecule will give up its hydrogen, and the stronger the acid. Thus, ternary acids are categorized according to the number of oxygens (relative to each other, the specific number does not have a direct effect on name). Any polyatomic ion ending in -ate changes inflection to -ic. For -ite, -ous. Acids with less oxygen than the -ous form attach the prefix hypo-, while acids with more oxygen than the -ic form attach the prefix per-. So, looking at chloric acid as an example:

Weakest  | HClO - hypochlorous acid
         | HClO2 - chlorous acid
         | HClO3 - chloric acid
Strongest| HClO4 - perchloric acid
         \/