The clustering coefficient is a measurement of the interconnection level of the neighbors of a node. It is a kind of all my friends know each other coefficient. A high clustering coefficient indicates that the node is part of a well-interconnected group (cluster), whereas if it is close to zero means that its neighbors do not connect to each other (star structure). Nodes with high clustering coefficient are, in some sense, expendable because they do not really affect the connectivity of their surroundings.
The following figure shows the clustering coefficient for a small network. Red nodes have high clustering coefficient and form a well-connected region of the network. On the other hand, blue nodes have zero clustering coefficient, so their neighbors do not know each other. Nodes with small clustering coefficient and high degree are key elements because they act as hubs on a network.