REST (Representational State Transfer) API is an architectural style for designing networked applications. It relies on a stateless, client-server communication protocol, typically HTTP, and it uses standard operations like GET, POST, PUT, DELETE to manipulate resources. REST APIs are designed to be simple, scalable, and easy to understand, making them popular for web services.

In the context of WordPress, the REST API allows developers to interact with WordPress websites programmatically. It provides a way to access and manipulate WordPress content using standard HTTP requests. Here's how it works and its use cases in WordPress:

1. Accessing Content: The REST API allows developers to retrieve WordPress content, such as posts, pages, categories, tags, comments, etc., in a structured format (typically JSON or XML). This enables integration with external applications, such as mobile apps or other websites.

2. Creating and Updating Content: Developers can use the REST API to create, update, or delete WordPress content remotely. For example, you can create a new post or update an existing post without accessing the WordPress admin dashboard directly.

3. Custom Applications: With the REST API, developers can build custom applications that interact with WordPress. For instance, you can create a mobile app that displays WordPress content, or a custom dashboard for managing WordPress content.

4. Headless WordPress: The REST API enables the concept of "headless WordPress," where the WordPress backend is used solely as a content management system (CMS), and the frontend is built using a separate technology stack, such as React.js or Vue.js. This approach offers more flexibility in design and development.

5. Integration with External Services: The REST API allows WordPress to integrate with third-party services and platforms. For example, you can integrate WordPress with an e-commerce platform for processing orders, or with a CRM system for managing customer data.

6. Automation: Developers can use the REST API to automate various tasks within WordPress. For example, you can create scripts to automatically publish new posts at specific times, or to perform regular maintenance tasks.

7. Data Migration: The REST API can be used for data migration between WordPress sites or between WordPress and other systems. This could involve transferring posts, pages, users, and other content from one site to another.

Here's a simple code example demonstrating how to use the WordPress REST API in a PHP script to retrieve a list of posts:

<?php

// Define the endpoint URL
$endpoint = 'https://your-wordpress-site.com/wp-json/wp/v2/posts';

// Make a GET request to the REST API endpoint
$response = wp_remote_get( $endpoint );

// Check if the request was successful
if ( is_wp_error( $response ) ) {
    // Handle error
    echo "Error: " . $response->get_error_message();
} else {
    // Decode the JSON response
    $posts = json_decode( wp_remote_retrieve_body( $response ) );

    // Check if posts were retrieved
    if ( ! empty( $posts ) ) {
        // Loop through the posts and display the titles
        foreach ( $posts as $post ) {
            echo "Post Title: " . $post->title->rendered . "<br>";
            echo "Post Content: " . $post->content->rendered . "<br>";
            echo "------------------------------------<br>";
        }
    } else {
        echo "No posts found.";
    }
}

In this example:

1. We define the endpoint URL for the WordPress REST API. This URL typically follows the pattern https://your-wordpress-site.com/wp-json/wp/v2/posts, where your-wordpress-site.com is your WordPress site's domain.

2. We use the wp_remote_get() function to make a GET request to the REST API endpoint.

3. We check if the request was successful using is_wp_error(). If there was an error, we handle it appropriately.

4. If the request was successful, we decode the JSON response using json_decode().

5. We loop through the array of posts retrieved from the API response and display each post's title and content.

This is a basic example, and you can extend it to perform other actions such as creating or updating posts by making POST or PUT requests respectively to the appropriate endpoints in the WordPress REST API. Additionally, you may need to authenticate your requests if you're performing actions that require authentication.