The Engagement shows an average amount of how often a fan interacts with the posts of a page. It is calculated by dividing the daily amount of reactions (likes, love, wow, haha etc.), comments and shares by the number of fans. If you are looking at a longer period of time it takes the average of the daily Engagement rates.
Example: Page A yields the following interaction values:
Monday: 20 interactions and 3500 fans
Tuesday: 0 interactions and 3590 fans
Wednesday: 37 interactions and 3700 fans
Thursday: 100 interactions and 3750 fans
Friday: 0 interactions and 3755 fans
Sunday: 2 interactions and 3783 fans
That leads to the following daily Engagement Rates:
Monday: 0.0057 (20/3500) or 0.57%
Tuesday: 0 (0/3590)
Wednesday: 0.01 (37/3700) or 1%
Thursday: 0.027 (100/3750) or 2.7%
Sunday: 0.00053 (2/3783) or 0.053%
For the whole week, we get the average Engagement value of: (0.0057+0+0.01+0.027+0+0+0.00053)/7 = 0.0062 or 0.62% That means, in this week each fan interacted 0.0062 times with the posts of the page.