In order to make requests to the Instagram API you first need to register an application (Instagram calls it a client). The developer section at Instagram.com lets you register a new client or simply manage existing clients.
An application has a client ID that is used to identify your app when making request to the API. An application also has a client secret that together with the client ID is used during authentication.
For endpoint methods that doesn't require a user context, the client ID is sufficient. This includes getting the media of a user with a known ID.