The Danes and the Brits pioneered graphic depictions of simple chemical reactivity. Brønsted and Lowry independently shocked early 20th century chemists with their notions of spontaneous self-ionization of water:
Brønsted-Lowry theory explains how even the purest distilled water conducts electricity (which requires something charged). In their scheme, one water acts like a base by accepting a proton, while the other one acts like an acid, donating a proton. The slight but measurable extent of such H-swapping is real enough--a normal glass of water has a measurable concentration of H3O+ of about 10-7 units or a pH of 7 (pH is like a Richter scale). An equal & countervailing amount of hydroxide, OH- neutralizes the acid.
Now consider adding anything to that glass of water which increases the amount of H3O+ (but not OH-). Such a thing which donates an H+ to a neutral water molecule is called an acid in English. The Germans call them Säure, which is related to our word sour. Svante Arrhenius (the august savant who also thought up AGW), came up with the idea first.