The traveling salesman is not a person but a problem in operations research. Its goal is to optimize (minimize) the traveling distance given a set of locations and distances between them while only going to each location once. It is actually a very computationally intensive problem (known as NP-Hard in combinatorial optimization). This problem can become even more complex if you add other considerations to the problem. It is not my intention to get to the technical aspects of the possible solutions but only to introduce the concept so that you are aware of it for conversation or to look deeper into it if you are interested. Here is a short YouTube video from AlphaOpt that explains it succinctly and helps visualize the problem.
It is obvious that minimizing distance traveled comes with benefits. You will save on fuel, driver costs, and equipment depreciation when you achieve the same result with less travel. You will also save time which directly affects supply chain performance. However, it is also important to keep in mind other factors that have not been worked into the pure Traveling Salesman Model. Why is travel being made? Is something being delivered or picked up? And what is the profitability for each location? Is there a time requirement/deadline for a location? Are there prerequisites or a certain sequence that has to be followed on the route? Does the rule of not returning to a location must apply? So as you can see, even though the problem is mathematically complex, the real world can be and is likely more complex.