When parents travel with a child under two years old, the child doesn’t need their own seat. A so-called ‘lap infant’ travels free when flying domestically. In general for international travel the lap infant will need a ticket, and so the parents have to purchase an ‘infant fare’.
Fortunately as of April 23, 2021 American Airlines no longer requires customers to pay more for their infant ticket when they upgrade which can mean a savings of hundreds of dollars – and a lot of headaches since the process used to be confusing.