Floyd's cycle-finding algorithm, also known as the "tortoise and hare" algorithm, is a method for detecting cycles in a sequence of values, such as linked lists. It uses two pointers that move at different speeds: one pointer (the tortoise) moves one step at a time, while the other pointer (the hare) moves two steps at a time. If there is a cycle, the two pointers will eventually meet. The algorithm is efficient, requiring only O(n) time and O(1) space, making it suitable for large datasets. It is widely used in computer science for problems involving cyclic data structures and is named after the characters in Aesop's fable.