A Complete Metric Space is a type of mathematical space where every Cauchy sequence converges to a point within the space. A Cauchy sequence is a sequence of points where the distances between points become arbitrarily small as the sequence progresses. This property ensures that limits of sequences are contained within the space, making it "complete." In simpler terms, if you take any sequence of points in a complete metric space and it gets closer together over time, you can always find a point in that space where the sequence will settle down. Examples of complete metric spaces include the set of real numbers, denoted as ℝ, and the set of complex numbers, denoted as ℂ.