Arrhenius theory is a classical acid-base theory that defines acids as substances that increase the concentration of hydrogen ions (H⁺) in aqueous solution, while bases are substances that increase the concentration of hydroxide ions (OH⁻). This theory, proposed by Svante Arrhenius in 1887, laid the groundwork for understanding acid-base reactions in terms of ionic dissociation in water, although it is limited to aqueous solutions and doesn't account for non-protonic acids and bases.