The Bellman-Ford Algorithm is a graph search algorithm used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. It can handle graphs with negative weight edges, making it more versatile than some other algorithms like Dijkstra's Algorithm. The algorithm works by repeatedly relaxing the edges, which means it updates the shortest path estimates until no further improvements can be made. The algorithm operates in O(VE) time complexity, where V is the number of vertices and E is the number of edges. It consists of V-1 iterations over all edges, followed by a check for negative weight cycles. If a cycle is detected, it indicates that no shortest path exists.