A Vertex Cover is a concept in graph theory that refers to a set of vertices in a graph such that every edge in the graph is incident to at least one vertex from this set. In simpler terms, if you imagine a network of points connected by lines, a vertex cover includes some of those points to ensure that every line is touched by at least one point in the cover. Finding the smallest possible vertex cover is a common problem in computer science and is known to be NP-hard. This means that there is no known efficient way to find the smallest vertex cover for all graphs, making it a significant topic in fields like algorithm design and combinatorial optimization.