A normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function. It is the most prominent probability distribution in used statistics.
Normal distributions are a family of distributions with the same general symmetric bell-shaped curve, with more values concentrated in the middle than in the tails. Two parameters describe a normal distribution, the mean, and standard deviation. The mean is the central location (the peak), and the standard deviation is the dispersion (the spread). Skewness and excess kurtosis are zero for a normal distribution.
The normal distribution is the basis of much statistical theory. Statistical tests and estimators based on the normal distribution are often more powerful than their non-parametric equivalents. When the distribution assumption can be met they are preferred, as the increased power lets you use a smaller sample size to detect the same difference.