Some airlines/airplanes have dedicated spaces for baby cradles/bassinets, usually placed in front of the seats at the border between plane sections. This is true in particular for long-haul flights, since the planes tend to be bigger. Each airplane has its own mounting system with the compatible bassinet. Below is a picture of what I am talking about:

These bassinets are usually installed during the flight, and are removed during take-off and landing. Often if the seat is taken by people who might not need the feature, these might be asked to move to another seat to accommodate parents and their infants. (I know I was asked to move many times.)