It means that the person is loud, fun, outspoken, and outgoing. It's not a bad thing at all but sometimes it can be annoying. It also means that the person is very attractive (looks and more) to others. The person could also have a very hot sex appeal. The person with a big personality will find him/herself surrounded by others seeking his/her company.
Guy 1: So what did you think of her?
Guy 2: Hot! She has a big personality! Wow!