// It took a while, but they are finally starting to cotton [ˈkɑtən] on.

// She quickly cottoned [ˈkɑtən] on to why her friend was nudging her, and stopped talking just before their teacher entered the room.

cotton
verb [ˈkɑtən]

The verb cotton is used with on or on to to mean “to begin to understand something; to catch on.” Cotton used with to alone means “to begin to like someone or something.”

The noun cotton, from the Arabic word quṭun or quṭn... until the early 20th century that someone who cottoned to or on to something had come to understanding...

English