As long as beer has been made, there has likely been sour beer. Now, it probably wasn't all purposeful, but since beer was being brewed before we had microscopes or knew what yeast was and it's impact on fermentation, most beers would have some level of sourness imparted by wild bacteria that assisted in fermentation. Sour beer is created by bacteria consuming the sugar in the freshly brewed wort (what will eventually become beer). When it consumes the sugar, one of it's byproducts is acid. Depending on what bacteria, it could be lactic acid or acetic acid, or many other (often less desirable) acids. The acid lowers the pH of the beer, creating a tart, puckering flavor and mouthfeel.