There are four major components of engagement in measuring social media engagement:
How users interact with your page through for example, CTAs
How users interact with your posts, whether it is retweets, likes or shares
How users interact with you via direct messaging
How you are mentioned on other pages
By looking at these four elements, it is possible to understand where your social media accounts may be failing and how improvements can be made.
Check out this informative article on Social Bakers, that looks at each element of engagement and shows how to increase overall engagement: