First of all, headstrong officially means "stubborn". But to me, I think of headstrong more in terms of standing up for what you believe in. In always being yourself, and being a nonconformist.
Being true to yourself and your standards is a value sometimes lost in our day. Sometimes we do what we think will make us more acceptable to society, or what will increase our social standing. What really matters though, is staying firm in our own beliefs. Don't let anyone sway you or tell you what is popular or right. You know what is right.
I think headstrong signifies the innate strength you have to blow the world away. To show everyone what one individual can do. That you, one tiny person in a huge world can take them all on, and show them who's boss. You have the ability and the talent to make the world a better place. To implement your own ideas to help benefit everyone else.
So be strong, and be yourself. In fact, be headstrong.