In the synthesis of drugs, crystallization is the cheapest method of purifying the final product and in most syntheses optimized by trial and error. This was the case with aspirin. Gerhardt received it in 1853, but it was not until Hoffmann purified it by crystallization in 1898.
The solubility of aspirin and salicylic acid in water at room temperature is similar - a few grams per liter. The solubility of aspirin in ethanol is much higher and salicylic acid dissolves much better. However, crystallization from pure ethanol does not give a sufficiently pure product.
Such a procedure was found experimentally: the crude product is dissolved hot in the least amount of ethanol, then hot water is added slightly below the temperature of the ethanol solution to turbidity, then some ethanol is added to the water-ethanol solution until the turbidity disappears and allowed to crystallize at RT, then at 0°C.