For a start it means you can much more naturally define arithmetic operators for a variety of built in and user-defined types, and this can all be done with libraries not the core language.

Because methods aren't "inside" objects, but just look like functions taking (references to) structs, you can add your own methods to someone else's types.

It's really hard to give a concise example that doesn't look artificial, because it's really a feature for large code bases.

Here's a tutorial example for Julia

https://scientificcoder.com/the-art-of-multiple-dispatch