I highly recommend by the late Hans Rosling: Why the world population won’t exceed 11 billion. It explains quite well what the sister comment by riffraff refers to.

[1]: https://www.youtube.com/watch?v=2LyzBoHo5EI

Wealthy people don't have many kids, as the average income goes up the number of kids per family goes down. Population has stopped growing in rich countries years ago, it is expected to happen in currently low income places too.

Access to better healthcare lowers the infant mortality rate. That than leads to couples having fewer children since they don't need to hedge their bets as much (ie having a more offspring expecting several to die). Combine that with easier access to contraceptives and you have some major reasons why birth rates decrease in developing countries which have the money to spend on healthcare.

In developed countries you may also have factors like people focussing on careers, valuing independence, more choice in relationships (i.e. divorce/separation being more acceptable) etc.