The normal distribution is the symmetric bell shape. Here the Empirical Rule applies.
It is important because it approximates well sample data in the real world and of its use in statistical inference.

The z-score represents the number of standard deviations that a value of a variable falls from the mean.

Z-scores provide a useful way to compare positions for different normal distributions. Find the probability by converting the z-score into the probability using a table of normal probabilities.

Covariance is the way that x and y vary together. If y tends to fall above its mean when x falls above its mean, the covariance is positive.

The population correlation equals the average cross product of the z-score for x times the z-score for y.