Prim's Algorithm is a method used in graph theory to find the minimum spanning tree of a connected, weighted graph. It starts with a single vertex and grows the tree by adding the smallest edge that connects a vertex in the tree to a vertex outside of it. This process continues until all vertices are included in the tree. The algorithm ensures that the total weight of the edges in the spanning tree is minimized. It is particularly useful in network design, such as connecting computers or roads, where minimizing costs is essential. Minimum spanning trees are important in various applications, including Kruskal's Algorithm and Dijkstra's Algorithm.