A connected component is a subgraph (a graph whose vertices are a subset of the vertex set of the original graph and whose edges are a subset of the edge set of the original graph) in which any two vertices are connected to each other by an edge or a series of edges.
An easy way to understand it would be by taking a look at the road network graph of Hawaii. This state has numerous islands, which are not connected by roads. Within each island, most roads will be connected to each other. The goal of finding the connected components is to find these clusters.
The connected components algorithm labels each connected component of the graph with the ID of its lowest-numbered vertex.
