The canonical example of the normal distribution given in textbooks is human heights. Measure the heights of a large sample of adult men and the numbers will follow a normal (Gaussian) distribution. The heights of women also follow a normal distribution. What textbooks never discuss is why heights should be normally distributed.
Why should heights be normally distributed? If height were a simple genetic characteristic, there would be two possibilities: short and tall, like Mendel’s peas that were either wrinkled or smooth but never semi-wrinkled. But height is not a simple characteristic. There are numerous genetic and environmental factors that influence height. When there are many independent factors that contribute to some phenomena, the end result may follow a Gaussian distribution due to the central limit theorem.
The normal distribution is a remarkably good model of heights for some purposes. It may be more interesting to look at where the model breaks down. See my next post, why heights are not normally distributed.