The Hadley children, Peter and Wendy, are characterized, both directly and indirectly, as being spoiled and selfish, though not through any particular character fault of their own. Their petulance is a side effect of their age and the overindulgences their parents have afforded them.
It is important to know that Peter and Wendy are visualizing Africa for a particular reason, which is not revealed until the end of the story; they are imagining their parents being murdered and eaten by lions. Thus, Africa itself has no particular bearing on the children's imaginations, and the were not visualizing Africa for itself, but for the fact that it provided a graphic way of imaginatively punishing their parents.
The children begin this fantasy because they are "accustomed to Santa Claus" - their parents have given them everything they want, and now they have no respect or obedience for their parents. The event which triggered their violent fantasies appears to be Mr. Hadley's denial of a rocket trip to New York, which he says they are too young for. He also shut off some of the machines in the house because the children weren't doing their homework. The children respond to these denials as one might expect children to, but the nursery affords them the gratification of seeing their fantasies come to life, which is why they keep it stuck on Africa for a month or more.