It's hard to say what that does, because pretty much every laptop has it's own special power connector. I can say that usually pins like you describe are used as ground pins. Not strictly needed, but they help to regulate the flow of power to the system. Ask an electrician if you want a more detailed explanation than that.
You should contact Acer about acquiring a replacement power transformer for the laptop. In the mean time, I would use the existing one sparingly. If possible, I would just shut the laptop off, and leave it that way until a replacement transformer can be obtained.
The bottom round prong for my wifes laptop broke off but tried and it is still keeping computer fully charged. We are sort of newbies. What is the round prong for? I'm pretty sure it is not safe so would have to get a new plug in for it and does it have to be from same company? It is an Acer aspire 3000 series. Thanks.