Data types in WordPress are interrelated: A post has an author, some number of tags, some number of categories, etc. By default, the API responses will provide pointers to these related objects, but will not embed the full resources: so, for example, the "author" property would come back as just the author’s ID, e.g. "author": 4.

This functionality provides API consumers the flexibility to determine when and how they retrieve the related data. However, there are also times where an API consumer will want to get the most data in the fewest number of responses. Certain resources (author, comments, tags, and categories, to name a few) support embedding, meaning that they can be included in the response if the _embed query parameter is set.

To request that the API respond with embedded data, simply call .embed() as part of the request chain:

wp.posts().id( 2501 ).embed()

This will include an ._embedded object in the response JSON, which contains all of those embeddable objects:

    "_embedded": {
        "author": [ /* ... */ ],
        "replies": [ /* ... */ ],
        "wp:attachment": [ /* ... */ ],
        "wp:term": [
            [ {}, {} /* category terms */ ],
            [ {} /* tag terms */ ],
            /* etc... */
        "wp:meta": [ /* ... */ ]

For more on working with embedded data, check out the WP-API documentation.