A story, song, or person that is engaging is entertaining, fun, and interesting — you want to see or hear more.
To remember the meaning of engaging, it might help to think of what engaged means. When a couple is engaged, they've agreed to get married. When something or somebody is engaging, you want to spend more time with them too. Boring is the complete opposite of engaging. Think of your favorite movie or TV show — especially one you can't stop watching — it must be very engaging.