The All Pairs Shortest Path algorithm is used to calculate the shortest path between all pairs of nodes in a graph, which can be useful for urban service system problems such as location optimization or distribution of goods. It's also used in data center design algorithms like REWIRE to find networks with maximum bandwidth and minimal latency. The algorithm has optimizations that make it quicker than calling Single Source Shortest Path for every pair of nodes, but returns infinity if no shortest path exists between two nodes. A Cypher query example is provided to calculate All Pairs Shortest Path on a small dataset, showing the top 10 pairs of nodes with the furthest distance from each other. The algorithm has applications in various fields and can be used for tasks like traffic load evaluation or network design optimization.