The central limit theorem states if you have a sample size large enough, usually 30 or above, you will have a normal distribution. As the sample gets larger, the more the graph will represent a normal distribution. This is fundamental in the world of research because it allows researchers to make inferences about data, if the sample is large enough, even if the distribution is not normal. I am not sure if the central limit theorem is necessarily the most important application, however, I saw a lot of websites discussing stocks and investments that use it to help assess risk. If you are investing, this could be a useful tool to see whether your decision to invest in stocks is a high risk or will potentially have a good return