In a way that powerfully attracts and holds someone's interest or attention; in a charming or compelling manner.
From captivating (the present participle of captivate) plus the adverbial suffix -ly, which describes how actions are performed or qualities are expressed.
Performers and speakers who work with captivatingly delivered material understand a secret: it's not what you say but how you hold attention while saying it—the delivery becomes the prisoner-taking mechanism.
Complete word intelligence in one call. Free tier — 50 lookups/day.