They offer interaction, so your sim has someone to talk to and doesn't feel isolated. I have a sim who is friends with her neighbour Penny Pizzaz and she comes over often, or asks my sim over to her place. You can hang out together and be friendly, and it's even funnier when you need to ask them to keep down woohoo noise when you're friendly with them. As for the interactions, they are different, one day Penny asked to be allowed to shower at my sim's place because her's was broken. With another sim, her neighbour asked her out. You can always create an interesting story with a neighbour, doesn't have to be only about angrily knocking on their door. I think asking a sim if they are a mermaid is meant to be an insult.
