Arrhenius' theory is useful because it explains acidic/basic behaviour really well in aqueous media. The theory says that acids in aqueous media produce H+ whereas bases produce OH- ions.
It clearly explains neutralisation reactions, where equal amounts of H+ and OH- when combined produce water. in this respect, it can also help in volumetric analysis such as titrations when equal moles of H+ and OH- when combined reach the equivalence point.
It also helps to clearly represent the strength of acids in solution - e.g. A 1M of HCl produces 1M [H+] whereas 1M CH3COOH produces less than 1M [H+].
.. also helps with concentration of acids/bases