The quality of being engaging; the characteristic of being interesting and holding someone's attention.
From 'engaging' plus the noun-forming suffix '-ness'. The root 'engage' traces back to Old French and ultimately means to pledge or commit, which evolved to mean to involve someone's attention.
This is one of those meta-words that demonstrates how English loves to turn adjectives into abstract qualities—'engagingness' is basically the noun form of the adjective describing what makes something worth engaging with!
Complete word intelligence in one call. Free tier — 50 lookups/day.