The short answer to your question is the following: If there is a non-significant correlation between two variables, it means that they are essentially independent, i.e., knowing the value of one variable does not provide any information about the other variable. For example, knowing the height of an adult does not provide any information about their IQ, so an adult’s height and their IQ are not correlated (or have non-significant correlation). However, if there is a weak correlation, between two variables, it means that when we know the value of one variable, we have some information about the other variable.
For example, if we listed the ages of 100 married men in one column of a table, and in the adjacent column, the corresponding ages of their wives, we would find that the two numbers in each row are very close, because people tend to marry those who are close to their own age. We would say that the age of a husband and his wife are positively correlated. Of course, we could not predict with certainty the age of the wife from the age of the husband, because some men choose much younger wives and some “cougars” attract much younger men. However, knowing the age of a husband does enable us to estimate the age of the wife.
To provide a measure of the predictability of one variable given the value of another (called the correlation), English Mathematician Karl Pearson, in 1896, defined a statistic called the correlation coefficient, that gives a measure of the strength of a correlation between two variables, such as height and weight, or age and net worth of a person. By entering a large number of values of paired variables into his formula for the correlation coefficient, we obtain a number between –1 and +1.
Pearson’s Mathematical Definition of Correlation (excerpt from Intelligence: Where we Were, Where we Are, & Where we’re Going)
A correlation coefficient of 0 indicates that the two variables are uncorrelated, i.e., totally unrelated. For example, the correlation between an adult’s height and IQ would probably be close to zero, since there is no evidence of a relationship between the two. On the other hand, temperatures expressed in both degrees Fahrenheit and degrees Celsius, have a correlation coefficient of +1, because a formula enables us to compute the value of either variable for any given value of the other. In describing the strength of a correlation between two variables, psychologists typically use the term weak for a correlation coefficient less than 0.3, moderate for a correlation coefficient from 0.30 to 0.49 and strong for a correlation coefficient of .50 or greater. For example, studies have shown that the IQs of siblings have a moderate correlation of about 0.47. (For the study showing the correlation between the IQs of siblings, see: Kaufman, Alan S. and Elizabeth Lichtenberger. 2006. Assessing Adolescent and Adult Intelligence (3rd ed.). Hoboken, NJ: Wiley.
