About: Strong Personality
A strong personality, at least to me, means that you always let your opinion be known whether it will be popular or not. You are not afraid to make your presence known. You are no "shrinking violet" and don't hold your tongue for any reason.
It may also mean that you are very outgoing, boisterous and enjoy attention. There is nothing wrong with this at all. As an introvert myself, I seem to always pick people with "strong" personalities as my dear friends. They seem to compliment my less-than-strong personality. I feel comfortable to be with someone who will speak up, say what I'm thinking but can't bring myself to say, make sure I'm noticed just by association.
A strong personality usually accompanies good or at least quick decision making abilities, not too worried about what others think of them, not afraid to say something controversial if they believe in what they are saying.
Some people consider a strong personality another way of saying overbearing, loud, obnoxious and if they're speaking of a woman...you can imagine a few of the words that "strong personality" conjures up in some minds. And sometimes, these are traits of someone who is considered to have a strong personality. It is not always a compliment - though it is also not always an insult. I think it depends on who you are asking and about whom you are asking.
I think some examples of people with strong personalities in which it is a compliment are, Bill Clinton, Oprah Winfrey, or even Simon Cowell (not always popular, but truthful and rather likable in my opinion.)
I think some examples of people with strong personalities in which it is not a compliment are, Kanye West (his personality is strong but shown mainly through rudeness), Kris Kardashian (no explanation necessary), some may say Hillary Clinton (no opinion to be stated here), and then there is someone like Dennis Rodman - I am unsure which category he would be in. Both, depending on his mood, I think would be the answer.
Strong personality probably means different things to different people. Overall, what I've said here is what it means to me and only to me. Though I imagine there is someone out there who might agree with me.