Analyticity refers to the property of a function that allows it to be expressed as a power series in a neighborhood of every point in its domain. In simpler terms, if a function is analytic, it can be represented by an infinite sum of terms, which makes it smooth and predictable. This concept is crucial in fields like mathematics and physics, where understanding the behavior of functions is essential. A key aspect of analyticity is that it implies the function is differentiable at every point in its domain. This means that not only can you find the slope of the function at any point, but you can also do so infinitely many times. Functions like polynomials and exponential functions are examples of analytic functions, showcasing their importance in various applications.