Headstrong describes something that's disobedient or willful. If you're headstrong, you want to do what you want to do. When you refuse to complete your homework because you want to watch a football game, you're being headstrong.
A closer look at the word headstrong can give you a hint to its meaning — the combination of the words head and strong. You're determined to have your own way because you have a strong belief that your view — what you have in your head — is the best one. Being a headstrong person is not always a bad thing. Sometimes headstrong people make history because they fight traditional values or outdated rules that need to be changed.