A Pythagorean Triplet consists of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2. This relationship is derived from the Pythagorean Theorem, which applies to right-angled triangles, where c represents the length of the hypotenuse, and a and b are the lengths of the other two sides. Common examples of Pythagorean triplets include (3, 4, 5) and (5, 12, 13). These sets of numbers can be used to create right triangles, making them useful in various fields such as geometry, trigonometry, and even computer science for algorithms involving distance calculations.