A planar graph is a type of graph that can be drawn on a flat surface without any edges crossing each other. This means that the vertices (or points) of the graph can be connected by edges (or lines) in such a way that no two edges intersect except at their endpoints. One important concept related to planar graphs is Kuratowski's theorem, which states that a graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph K5 or the complete bipartite graph K3,3. Planar graphs have various applications in fields like computer science, geography, and network design.