Prim
In plain terms
Grows a minimum spanning tree outward from a starting node.
Going deeper
Prim's algorithm starts at one node and repeatedly adds the cheapest edge connecting the tree to a new node. It builds the MST incrementally.
Under the hood
O(E log V) with a heap; better than Kruskal on dense graphs since it grows one connected component.
Examples
Minimum spanning trees, network/utility design, dense-graph MSTs.
Think of it like...
Like expanding a power grid one cheapest new connection at a time from a central plant.