You know or should know that an acid, HXHX, is a proton donor in some solvent, typically water.....and we could represent its characteristic reaction in the following way....
underbrace(HX(aq))_"parent acid" + H_2O(aq) rarr underbrace(X^(-))_"conjugate base" + underbrace(H_3O^+)_"hydronium ion"
The hydronium ion is a conceptual species; it is a cluster of water molecules, 3 or 4 or more to give say H_7O_3^+, with an EXTRA H^+..we write H^+ or H_3O^+ as a shorthand....
H_3O^+ is the so-called "CONJUGATE ACID" of water, i.e. the original acid PLUS a proton...of course we conserve mass and charge. And HO^- is the so-called "CONJUGATE BASE" of water, i.e. the original acid MINUS a proton.
And using this formalism, all strong acids react in solution to give their "CONJUGATE BASES". What are the conjugate bases of HClO_4, H_2SO_4, HNO_3?
To go to another example...what is the conjugate acid of NH_3. I make it NH_4^+ (and I hope you do too). But what is the conjugate base of ammonia? This is so strong a base that it does not occur in water, but DOES occur in liquid ammonia.
Confused yet? But all I have done is to add or subtract protons, H^+, and CONSERVED CHARGE and MASS.....
See here and links for further examples.