Arrhenius measured the conductivity of highly pure samples of water. Because even the most pure samples retained a conductance, Arrhenius proposed an equilibrium between charged particles, and base solvent...........
#H_2O rightleftharpoonsH^(+) + HO^-#
#H^+# was conceived to be the #"acidium ion"# and the corresponding base was #HO^-#. As with any chemical equilibrium, its position could be manipulated by the addition of reagents which increased concentration of EITHER species. The equilibrium itself was a constant, dependent on temperature, and we still write.......
#K_w=[H^+][""^(-)OH]=10^(-14)# under standard conditions of temperature and pressure. Now this is a very powerful definition, so much so that it is still used today, and by students (a true testament to Arrhenius' insight!), but it was supplemented by an alternative definition of acids and bases that was proposed independently by Joh Brønsted and Thomas Lowry. They conceived acid-base behaviour on the basis of proton transfer between solvent molecules:
#2H_2Orightleftharpoonsunderbrace(HO^(-))_("the conjugate base")+underbrace(H_3O^(+))_("the conjugate acid")#
Acid and base differed on the basis of proton transfer to or from the mother solvent. A weak base (one which was loosely bound to the proton corresponded to a strong conjugate acid, and a strong acid corresponded to a WEAK conjugate base. And thus a strong acid is conceived to protonate the water solvent, and form the #"hydronium ion"#, a conceptual species:
#HX(aq) +H_2O rightleftharpoons H_3O^+ + X^(-)#.
As far as anyone knows the actual acid species, which is represented as #H_3O^+#, is a cluster of several water molecules, 3 or 4, with an EXTRA #H^+#, i.e. #H_7O_3^+# or #H_9O_4^+#, i.e. #H_3O^+# for simplicity. For one example of how this is quantitiable see here.