What does it mean to have a normal distribution of data?

The Normal or Gaussian distribution is a probability distribution which depends on two parameters: the mean and the variance (or standard deviation). In may real life situations measurements are found to be approximately normal. Furthermore, even if the underlying distribution of a variable is not normal, the mean of a number of repeated observations of the variable will approximate the normal distribution.

The term "approximate" is important because, although the heights of adult males (for example) appear to be normally distributed, the true normal distribution must allow negative heights whereas that is not physically possible!