I've always tried to avoid Webpack. I would tell myself it was either too complicated or unnecessary. After all, it's not the only tool of its kind on the market. Recently, however, I've come to terms with Webpack. Once you know how to use it comfortably, it can be a very effective tool.
require. Bundling can also take care of features which may not be compatible with all browsers, such as es6 notation. This requires the babel plugin.
You can preprocess scss. There are other ways such as gulp, node-sass and even a VS Code extension, but once you're using webpack this is a pretty useful feature. This requires a [webpack loader].
You can compile jsx for ReactJS. This is can be easier to set up in some situations, especially in a complex environment such as an electron app. There's a good tutorial on compiling jsx with webpack here. Note that this requires a plugin as well.
You can compile typescript with it. Admittedly, you can compile typescript within VS Code, however it's useful, because you can do two things with one command such as compile scss and typescript. This requires a plugin.
You can run a development server with your static files. There are extensions to do that, but it can prove useful when running multiple tasks or complicated setups. This requires an extra package.
Did I miss anything that eases your workflow? Let me know in the comments.