This algorithm is another one approach to find the MST - minimum spanning tree. The main idea is to partition a set of vertices into two: included to MST already and excluded. Step by step you’ll replace vertices from the second set to the first by picking the less weighted edge that connects both sets.

So algorithm is next:

1. Put the start vertex to the visited, the rest will be unvisited, i. e. in the second set.

2. Start adding vertices. Visit all neighbors for all visited vertices and select the edge with least weight, that does not create a cycle. Mark the adjacent vertex as visited.

3. Do the 2) until all vertices are visited.

You can find a lot of different implementations, but the main idea is to put all vertices into the visited set step by step.