You can think of it as the estimate for the standard deviation of the error term. If you multiply it by 2, you can use the empirical rule to make a statement that about 95% of the actual y values will fall within 2*s of their respective predicted values using the particular model (within 2*s implies above and below the average, hence the approximate interval). It gives you a bit of an idea about accuracy, if only in-sample. If you find that 2*s is too large, you may want to find a way to improve the model.