Vue.js leverages the Virtual DOM (VDOM) and a reactivity system to efficiently update the UI based on data changes. Here’s a brief explanation of how these mechanisms work:

1. Virtual DOM (VDOM): The Virtual DOM is an abstraction of the real DOM provided by the browser. It’s a lightweight JavaScript representation of the actual DOM elements. When you modify data in Vue.js, it doesn’t directly manipulate the real DOM. Instead, Vue.js updates the Virtual DOM first.
2. Template Compilation: Vue.js compiles the template of each component into render functions. During compilation, the template is parsed and transformed into a render function that generates Virtual DOM elements. This process optimizes the rendering performance by avoiding the need to parse the template on every update.
3. Reactivity System: Vue.js uses a reactivity system to track data changes and update the Virtual DOM accordingly. When you define a data property in a component, Vue.js wraps it in a getter and a setter. These getters and setters allow Vue.js to observe changes to the data properties.
4. Dependency Tracking: When a component’s render function is executed, Vue.js automatically records which data properties are accessed during the render. This establishes a dependency relationship between the component and the data properties it relies on.
5. Reactive Updates: When a data property that a component depends on changes, Vue.js triggers a re-render of that component. It compares the new Virtual DOM with the previous one and calculates the minimal set of DOM manipulations needed to bring the UI up to date.
6. Diffing Algorithm: Vue.js uses a Diffing Algorithm to efficiently update the real DOM based on the changes in the Virtual DOM. It compares the new Virtual DOM with the previous one and only updates the necessary parts of the actual DOM, minimizing the number of DOM operations and improving performance.
7. Patch Operations: The Diffing Algorithm performs patch operations on the real DOM to apply the necessary changes. It adds, removes, or updates DOM nodes as required to match the new Virtual DOM structure.

By using the Virtual DOM and the reactivity system, Vue.js achieves efficient updates to the UI, reducing the amount of direct interaction with the real DOM and optimizing performance. These mechanisms allow Vue.js to provide a smooth and reactive user experience while keeping the development process simple and declarative.