It is certainly important that the person wants to do it for themselves first. You may be surprised how many of my clients tell me that they have a goal in mind but there is something about their body language and tone of voice that suggests otherwise. Very often it becomes established that the goal isn't theirs at all but somebody else's (usually a parent or coach). This is where you end up with 'pushy parent' syndrome where a parent is living their own dreams vicariously through their children and their children end up pursuing something that they would rather not. The problem with striving for a goal for someone else is that eventually any motivation to train, learn and develop your skills will turn to resentment, lack of drive and, often, fear of failure (not wanting to let people down) which all make achievement far less likely.
For a goal to be successful it is essential that it is your own goal. However, to make a goal even more likely (and to make it more fulfilling) it is much better to have a reason which is bigger than yourself to do it. This is very different to doing it for somebody else. This is about having a purpose or a mission to strive for. Purpose takes many forms and can essentially be anything that you feel to be really important. Examples could include wanting to do something for your country or community, doing something for a charity, for religious reasons, to reflect a certain philosophy, overcoming adversity, to be the best at something or to do something that has never been done before.