The smaller the standard error, the more representative the sample will be of the overall population. And the more data points involved in the calculations of the mean, the smaller the standard ...

The equation for the standard error of the mean is the sample standard deviation divided by the square root of the sample size.

Standard deviations are important here because the shape of a normal curve is determined by its mean and standard deviation. The mean tells you where the middle, highest part of the curve should go.