According to Johannes Nicolaus Brønsted and Thomas Lowry,
An acid is a substance from which a proton can be removed.
A base is a substance that can remove a proton from an acid.
Reduced to its essence the definition specifies that an acid only exists as an acid in relation to a base, and vice versa. This definition was arrived at more or less simultaneously in 1923 by these two researchers.
Johannes Nicolaus Brønsted (1879-1947)
and Thomas Martin Lowry (1874-1936)
Brønsted wrote an article announcing his views on the theoretical explanations of acids and bases, whereas Lowry wrote a long letter to the editor of the Journal of the Society of Chemical Industry, serenading the uniqueness of hydrogen.
The superiority of this definition to the earlier Arrhenius definition lies in its avoidance of the dissociation absurdity.
At no stage is one invited to believe that a 1-molar solution of hydrochloric acid contains 1 mole of protons, whirling around looking for skin to dissolve. Instead, the acid transfers the proton to another molecule, which acts as a base (i.e. a proton acceptor); the transaction is as rapid as laws of physics would permit, and the protons only exist in isolation for a ludicrously small period of time.
This also allows the incorporation of a solvent into the equation, as a basic (or acidic) participant.
HA + H2O → H3O+ + A-
Thus, the acid HA actually contains a "conjugate base", i.e. the A- which holds the proton in the absence of a solvent. The water in this equation, being the solvent, acts as a more powerful base, stripping the proton from the acid. The conjugate base and acid pairing is a key concept of this model, which has survived the actual model - today, we can describe lactate in Hartmann's solution as a conjugate base of lactic acid.
The theory thus opens the possibility of amphiprotic substances, i.e. those which may either donate protons, or accept them.
Problems with the Brønsted-Lowry definition of acids and bases
Though popular, and appropriate for the purposes of bedside medicine, this definition remains unsatisfying to the sort of person who would casually read Pure and Applied Chemistry.
There are several reasons for this.
The theory has no definition of neutrality
In the old Arrhenius definition of acids and bases, at least you could make the claim that a solution is neutral when the concentration of H+ ions is the same as the concentration of OH- ions. That was a pretty satisfying definition of neutrality- equal amounts of acid and base. With their abandonment of proton concentrations, Brønsted and Lowry also lost their access to this definition.
The theory is still concerned with the traffic of protons
Though no longer interested in describing whole swarms of protons, there is still the reliance on protons exchanging dance partners. This does not explain the behaviour of "aprotic" solutes such as CO2 or SO2, which behave as acids in spite of having no proton to donate. Some of these don't even require a solution to react (eg. CaO + SO3 → CaSO4 occurs in the absence of a solvent)
The theory still favours polar solvents
Non-polar solvents, which are thoroughly disinterested in participating in proton-related games, are excluded from this definition. Thus, the model fails to explain what happens to an acid which is dissolved in acetone. In 1923, around the time of Brønsted and Lowry's publication, Gilbert Newton Lewis wrote:
"We are so habituated to the use of water as a solvent, and our data are so frequently limited to those obtained in aqueous solutions, that we frequently define an acid or a base as a substance whose aqueous solution gives, respectively, a higher concentration of hydrogen ion or of hydroxide ion than that furnished by pure water. This is a very one sided definition."
Lewis' objections to the neglect of aprotic solvents had resulted in a yet more sophisticated definition, which together with the Brønsted-Lowry model has become incorporated into the repertoire of modern chemistry.