The Perfect Graph Theorem states that a graph is perfect if, for every induced subgraph, the size of the largest clique equals the size of the smallest coloring. This means that in a perfect graph, the chromatic number (the minimum number of colors needed to color the graph) matches the size of the largest complete subgraph (clique) found within it. This theorem was proven by László Lovász in 1972 and has significant implications in graph theory and combinatorics. It helps in understanding the structure of graphs and has applications in various fields, including computer science and optimization.