The Konigsberg bridge problem involves finding a walk through the city of Konigsberg that crosses each of its seven bridges exactly once. Euler simplified the problem by modeling it as a graph with four vertices (land areas) connected by seven edges (bridges). He determined that since the graph contains four vertices with an odd number of edges, it is impossible to traverse the graph using each edge exactly once. This negative solution to the Konigsberg bridge problem laid the foundation for the field of graph theory in mathematics.