A normal distribution is completely symmetrical, a skew distribution is not.
In a positively skewed distribution, the "toe" at the larger side is longer than at the other side, causing the median, and especially the mean, to move to the right. In a negatively skewed distribution these move to the left, because of a longer "toe" at the smaller values.
While in a non-skewed normal distribution mode, median and mean are all at the same value.
(pictures from internet)