The sample mean, x is the point estimate for the population mean. A 95% confidence interval is used to express how confident we are that the true population parameter lies within the confidence interval, NOT 95% probability.
In the given problem, the lower limit of the average is 10.1, while the upper limit is 31.1.
This means that with 95% confidence, the mean width of a randomly selected widget will be between 10.1 and 31.1.