In the case of web components, there is a fundamental problem that makes widgets built out of HTML and JavaScript hard to use.
Problem: The DOM tree inside a widget isn’t encapsulated from the rest of the page. This lack of encapsulation means your document stylesheet might accidentally apply to parts inside the widget; your JavaScript might accidentally modify parts inside the widget; your IDs might overlap with IDs inside the widget and so on.
Shadow DOM addresses the DOM tree encapsulation problem.
For example, if you had markup like this:
<button>Hello, world!</button>
<script>
var host = document.querySelector('button');
var root = host.createShadowRoot();
root.textContent = 'こんにちは、影の世界!';
</script>
then instead of
Hello, world!
your page looks like
こんにちは、影の世界!
Not only that, if JavaScript on the page asks what the button’s textContent is, it isn’t going to get “こんにちは、影の世界!”, but “Hello, world!” because the DOM subtree under the shadow root is encapsulated.
NOTE: I have picked up above content from https://www.html5rocks.com/en/tutorials/webcomponents/shadowdom/ as it helped me understand shadow DOM a little better than answers already here. I have added relevant content here so that it helps others but do take a look at the link for detailed discussion on same.