Different places in the world/engage her

Sorry for this question, but I don't understand if the mother and the baby are at a room, why they say "world"? (At 0:43 video)

My second question is what is "to engage her" in other words, please? Thanks.

Are you my good girl? Oh, yes… And she gives a greeting to the baby, the baby gives a greeting back to her. Dah! This baby starts pointing at different places in the world and the mother is trying to engage her and play with her.