The Cauchy Integral Formula is a fundamental result in complex analysis that provides a way to evaluate integrals of analytic functions over closed curves. It states that if a function is analytic inside and on some simple closed curve, the value of the function at any point inside the curve can be expressed as an integral of the function over the curve, divided by the distance from the point to the curve. This formula is significant because it not only simplifies the computation of integrals but also leads to important results, such as the Cauchy Integral Theorem and the concept of analytic functions. It highlights the deep connection between complex integration and the properties of holomorphic functions.