The Floyd-Warshall Algorithm is a method used in computer science to find the shortest paths between all pairs of vertices in a weighted graph. It works by systematically considering all possible paths through the graph and updating the shortest path estimates until no further improvements can be made. This algorithm is particularly useful for dense graphs where many vertices are interconnected. The algorithm operates using a dynamic programming approach, iterating through each vertex as an intermediate point. It has a time complexity of O(V^3), where V is the number of vertices, making it efficient for smaller graphs but less suitable for very large ones.