Drop a stone in water and watch the ripples spread. The water closest to the stone moves first. Then the next ring moves, then the next. Each ring is the same distance from the center. BFS works exactly like this. Start at node . First, visit all nodes that are step away.
Then visit all nodes that are steps away. Then steps, and so on. By the time you reach a node, you have already visited all closer nodes. This guarantees the first path you find is the shortest path. The ripple pattern is the core observation behind BFS.