Two variables are said to be closely correlated if there is a strong relationship between them. Suppose you wanted to test the relationship between height of parents and their children, and you had gathered the necessary data.
You could plot parent heights vs child heights on a graph and draw a line through the points by eye. Alternatively you could use 'regression analysis' to find mathematical equation for the line of best fit.The resulting equation is the 'regression equation'. You should then use correlation analysis to determine:
 whether there is a meaningful relationship, or whether any apparent relationship could be explained by chance
 whether parent height was the only important factor or only had some degree of influence
If there was a strong tendency for tall parents to have tall children there would be a strong positive correlation. If there was a strong tendency for tall parents to have short children, and short parents to have tall children there would be a strong negative correlation. If the height of the parent made no difference there would be no correlation. I have never seen data on that particular relationship, but I would guess that there is a weak to moderate positive correlation, there is some tendency for tall parents to have tall children, but there are many other factors at play.
Note that 'correlation' does not imply 'causation'. Countries with low levels of female literacy tend to have high fertility rates. However there is no causal relationship between literacy and fertility.
For more information see Pearson's Correlation Coefficient (R) and Coefficient of Determination and Regression Analysis.
