The correlation coefficient (r) tells you the strength of the relationship between two variables. The value of r has a range of -1 to 1 (0 indicates no relationship). Values of r closer to -1 or 1 indicate a stronger relationship and values closer to 0 indicate a weaker relationship. The coefficient is affected by a variety of factors, so it's always best to also plot your two variables as a scatterplot.
A relationship between two variables might be correlated - like ice cream sales and murders committed on a particular day. This does not mean that people buying more ice cream CAUSES murders to increase. A relationship like this is called a spurious relationship or a spurious correlation.
Regression is a statistical method that tries to uncover the association between variables. There are assumptions that must be met before running a regression and it's very important to understand how to properly interpret a regression equation. There are methods for how to find which predictors are best such as the bootstrap method, and there are others who will choose predictors based on theory.