'Engagement' is open to interpretation but for the purposes of this post and in the context of a website, it means how well your site captures people's attention and encourages them to do something – be it read content, push buttons, fill out a form, make a comment etc.
So, how do you know? You can't actually measure how engaged a person is, but you can infer it by what they do on the website. And how do you measure it? - enter Google Analytics statistics
Of course you need to be clear about the goals of your website and how you want people to use it to really understand how you are doing and what your engagement statistics mean. Everything may not be what it seems at first glance.