Importance: That highest third of our standards and priorities that gets acted upon or thought about first. The significance of this third to us creates in part the personality committments we will make or turn away. Yes this creates a definitional loop around here.
To climb out of the loop, it is necessary to look for a common cause(s) for these two things since both are about the ordering of preferences, or the deciding of what is important and what is less so. [Fleiss purrrups and the plants all look up.] In the mean time, back to the original idea.
How do we decide what is important and what is not? Let's say there is a default set no matter when we are in our lives. We are born witha default set of preferences, and although we may alter these, we always have something ther to assist in decidings. The altering of the system is of course more interesting than leaving the set as it was created by the nuture / nature thing. I always add a third even if it may be derivitive of the first two: self-awareness. Of course either of nature or nuture might play a role in creating self-awareness, but I do claim that once started, self-awareness takes on a journey of its own, one of sentience. How and why people both might become self-aware, but they will act differently in accordance with this: reporting on one's internal states versus altering one's internal states is the basic difference (in this week's version of the theory).
This default reaction or evaluation provided by our default settings will allow us to sift through what is to get to what is important. It also allows us to sift through it to get at whether the default itself is properly representative of what we want or need in the world. I see no reason to assume that the default settings one arrives with are in order, but those who had happy lives all along will disagree. C'est la vie.
What should be important? Heh. To me it is fame and fortune, friends and my family: Hella and Peter, Richard and Tracey. Oh, and methods for getting exactly what I want out of this finite existence.