What makes something an acid, and why did Lavoisier get it wrong?

An acid is a substance that donates a proton, and a base is one that accepts it. That is the Brønsted-Lowry definition, proposed independently by Johannes Brønsted and Thomas Lowry in 1923. An older definition, from Arrhenius, said that acids give H+ in water and bases give OH- ions. Acetic acid is an acid because it donates a proton to water, and water is a base because it accepts it. In the same year G. N. Lewis offered a broader view based on electronic structure: a Lewis base gives an electron pair to a Lewis acid, which accepts it.

The idea needed several corrections. Antoine Lavoisier coined the name oxygen from Greek words meaning acid former, because he held that all acids contained oxygen, and that later turned out to be wrong. Chlorine's discoverer, Scheele, had mistakenly thought it contained oxygen, and it was called oxymuriatic acid. Humphry Davy showed that it contained no oxygen, and in 1810 he insisted that chlorine was an element. Hydrochloric acid, a solution of hydrogen chloride, HCl, is made of hydrogen and chlorine alone. Lewis later wrote that restricting acids to hydrogen-containing substances would hinder chemistry as much as restricting oxidizing agents to substances containing oxygen.

The definition is relative. In Brønsted-Lowry theory an acid is only an acid in relation to a base, and water, which can act as either, is amphoteric.

The pH scale measures the result. Sørensen introduced it in 1909 at the Carlsberg Laboratory, and since it is logarithmic, a difference of one pH unit is a tenfold difference in hydrogen ion concentration. Pure water at 25 degrees Celsius sits at pH 7, and blood is usually slightly alkaline at 7.365.