A normal distribution is a theoretical distribution of data that are applied to continuous random variables. Most commonly called the Bell Curve (Broyles, 2006). The normal distribution is perhaps the most important theoretical distribution applied to data as it sets the stage for what to base our analyses off of. Using the normal distribution, we can identify what a standard deviation is, and where the data that is being analyzed falls in respect to standard deviations.
I believe the normal distribution is critically important because it is the basis for all of the data analysis performed on any given study. Without having a concrete base to work with, the analysis would fall apart.
References:
Broyles, R. W. (2006). Fundamentals of statistics in health administration. Sudbury, MA: Jones and Bartlett. ISBN-13: 9780763745561. Retrieved from http://gcumedia.com/digital-resources/jonesandbartlett/2006/fundamentals-of-statistics-in-health-administration_ebook_1e.php