Vertex connectivity is a measure of how well-connected the vertices in a graph are. Specifically, it refers to the minimum number of vertices that need to be removed to disconnect the remaining vertices from each other. A higher vertex connectivity indicates a more robust graph, as it can withstand the removal of several vertices without losing overall connectivity. In a graph with a vertex connectivity of zero, removing any single vertex can lead to a disconnected graph. Conversely, a graph with high vertex connectivity remains connected even after the removal of multiple vertices, making it more resilient to failures or attacks.