It’s a bit of third-party code that extends the capabilities of a website. It extends the functionality without having to redo the core coding of the site. One of the more common plug-ins is Adobe Flash Player. Without Flash Player you won’t, for example, be able to view BBC News bulletins embedded into web pages.
Other plug-ins are available for different things. There are plug-ins for social media networking, foreign language alphabets and many other things.