According to the work of Svante Arrhenius;
An acid is any substance which contributes hydrogen ions (H+) to the solution.
A base is any substance which contributes hydroxide ions (OH-) to the solution.
Svante August Arrhenius
(1859 – 1927)
This definition was the result of early research by Svante Arrhenius whose 1884 doctoral thesis concerned the dissociation of electrolytes. The research and analysis had ultimately earned him the Nobel Prize for chemistry in 1903.
Arrhenius' century-old definition is actually the definition one will get when one walks around asking random medical staff to define what an acid is.
The concept is reinforced by the education system which insists that
HA → H+ + A-
This, according to at least one author, is a failure on the part of the education system. The definition is outdated and there is a good argument that it should no longer be used to poison the delicate minds of chemistry students. Though the concept was true for most of the acids and bases known at the time, even early in its history there was concern that as a definition it was unsatisfactory.
Several issues with the definition must be acknowledged, so that it may meet with popular derision, and through ridicule become replaced by a more robust definition.
Contrary to popular belief, hydrogen ions are not a real constituent of a solution. To be sure, an instantaneous snapshot of water may reveal some protons lurking between the molecules; however the proton affinity of H2O is massive - about 700 kJ/mol - which means the union of H+ and H2O (forming the "hydronium ion", H3O+) is massively favoured by the laws of thermodynamics. The proton is therefore a true rarity in an aqueous solution, as it is immediately absorbed. This was described by Lowry (of Brønsted-Lowry fame) as "an extreme reluctance of a hydrogen nucleus to lead an isolated existence". A team of chemistry teachers has posted a value estimating the true concentration of H+, which they report as being in the range of 10-130 moles/L.
Arrhenius' model does not take into account any solution other than the aqueous. The solvent is merely an unseen backdrop for the equations. However, obviously dissolving an acidic substance in a solvent with bizarre properties (eg. kerosene or liquid helium) will give rise to a solution with vasty different acidity when compared to water.
A salt dissolving in water should- according to Arrhenius - give rise to a perfectly neutral solution, as neither H+ nor OH- are being contributed. However, this is not the case; for instance salts that contain anions derived from weak acids form solutions that are basic.