Vizing's theorem is a fundamental result in graph theory that deals with the coloring of edges in a graph. It states that for any simple graph, the chromatic index, which is the minimum number of colors needed to color the edges so that no two adjacent edges share the same color, is either equal to the maximum degree of the graph or one more than that maximum degree. This theorem is significant because it helps in understanding how to efficiently assign resources or tasks in various applications, such as scheduling and network design. It provides a clear guideline for determining the edge-coloring properties of graphs, which are essential in many areas of computer science and mathematics.