Reading an example tells you what a response looks like. Running it lets you see what happens with your own request.
The IP docs have a Run button next to the response. For this request, the API looks up the address you're connecting from:
GET /ip
Press Run and the sample is replaced with the live response. The page shows the time measured in your browser and the region that answered. The User-Agent example works the same way, using the browser you're reading the docs in.
When you're signed in, the curl examples also fill in your key, so you can copy the request without replacing YOUR_API_KEY first.
Lookups with a separate charge and paid profile details stay static. The Run button supports basic lookups and optional details that are included on every plan, such as Phone and Time ?deep=true. It lets you check the result before moving the request into your own code.