Breadth-first search (BFS) is a technique for traversing graphs where the algorithm starts at a root node and explores all neighboring nodes at the present depth prior to moving on to the nodes at the next depth level. BFS guarantees to find a solution if one exists and to find the shortest solution path. An example shows using BFS to find the shortest path between two nodes by exploring all adjacent nodes at each level before moving deeper in the graph. Applications of BFS include finding shortest paths and checking for bipartiteness in graphs.