jQuery is a fast, small, and feature-rich JavaScript library that simplifies HTML document traversal and manipulation, event handling, animation, and Ajax interactions for rapid web development.

1. DOM Manipulation: Easily select, traverse, and modify HTML elements using concise syntax (e.g., $(selector)).
2. Event Handling: Attach and handle events (like clicks, mouseovers, key presses) on elements in a consistent way.
3. CSS Manipulation: Easily apply, remove, and toggle CSS classes and styles.

1. Concise Syntax: jQuery provides a more concise and readable way to write JavaScript code, reducing the amount of code needed for common tasks.
2. Cross-Browser Compatibility: jQuery handles many of the cross-browser inconsistencies, saving developers time and effort.
3. Large Community and Ecosystem: A vast community and a rich ecosystem of plugins and extensions provide ample resources and solutions for various development needs.

1. Creating interactive web pages: Handling user interactions, dynamically updating content, and creating animations.
2. Building Ajax applications: Making asynchronous requests to servers to retrieve data and update the page without full reloads.
3. Developing single-page applications (SPAs): Creating dynamic and responsive web applications that update content without full page reloads.