What does “安安” mean? Several people have said it in a chat, but I don’t think it’s a way of laughing?

I doubt you might hear ān ā (安啊) from a Taiwanese people, because ān ā is a popular term here having a meaning of safe, pass (an exam, course, etc.), done.
As to 安安，it is a popular nickname for child, a company name or a brand name. If someone uses it in conversation, it’s just his or her personal habit to say something or someone he/she has positive feeling.

It means "An"

Sorry, I don't speak Chinese. Maybe go online to a translation site.