Here's an example of NPX in action: npx cowsay hello
If you type that into your bash terminal you'll see the result. The benefit of this is that npx has temporarily installed cowsay. There is no package pollution since cowsay is not permanently installed. This is great for one off packages where you want to avoid package pollution.
As mentioned in other answers, npx is also very useful in cases where (with npm) the package needs to be installed then configured before running. E.g. instead of using npm to install and then configure the json.package file and then call the configured run command just use npx instead. A real example: npx create-react-app my-app