How does ML Clustering put to a practical real-world use?
You want to understand the data.

So you run a clustering, then study how the points in a cluster differ from the points not in a cluster. Then based on these observations, you form a hypothesis. For example, you may notice that a cluster contains countries who eat a lot of fast-food and who are overweight. Then you can formulate the hypothesis that fast-food causes overweightedness, and then test that hypothesis.

This is a form of explorative data analysis. There is not a mathematical function to maximize, but it is a tool for humans to understand their data and then be able to formulate new hypotheses that would not have sprung to your mind otherwise.