When we look at engagement as a metric we are looking for users that are engaging with your website. As stated in the Oxford English dictionary "engaging - interesting or pleasant in a way that attracts your attention." We all try to aspire to this with our website's, making them so that users find it pleasing and interesting.
The issue with engagement as a metric is the context of the measurement, it is virtually impossible to gauge if engagement relates to a positive or negative experience on your site.
Engagement metrics should always be taken with a pinch of salt, they should only be used to give you a rough idea of how users interact with your site, the fact that it is virtually impossible to understand the context (positive or negative experience) of the visit makes it a tricky metric to work with