What is the main benefit of including CSS in an external file?

The benefits and drawbacks would depend on the size of the project. If you're just doing a simple one-page site (e.g landing page) then there's probably not any real benefits.

However, most websites and web applications are quite large and separating the markup from the layout is always a good idea, because it makes the different aspects of the site more easily manageable.

Another benefit is that you can use the same css file for multiple html pages, simply by just importing it within each page. If you were to do in-line css or embedded css, you'd end up with bigger files and if there's a global style you'd want to change in the future, you'd have to open each file and change it one-by-one.

Really, you should virtually always use external css whenever possible, and only use embedded or in-line css when needed in an edge-case scenario.

The reasons are many, and the examples are endless. I suggest googling this question if you need more in-depth examples.