have been with mvc for a little while. the usual case when an action returning json, it is initialized by ajax in the view and the view is expecting info inside the json.
Yes, a JSON API can be consumed by a large variety of clients. It can be the browser sending an AJAX request, but it can also be a desktop application fetching data from the Internet, a server-side job scraping the data for analysis, etc.
For example, let's say you're running a stock exchange website, and you're publishing current stock values as JSON. You can use that JSON on your website to display the data, but you (or any other developer) can also write a desktop application which will get that data and process it on a local machine (to, for example, show the user which stocks they should buy). Or aggregate data from different sources.
Many websites make their APIs public, so that third party developers can write alternative clients, integrate the API's functionality in their own products, and so on. For example, GitHub's APIs are public - the GitHub website can utilize them for the AJAX requests, and GitHub for Windows can show you the list of repositories you own by making a request to that API using C#'s WebClient.