I agree with a lot of what has already been said. Innovation, achieving your dream, duality, nature, et cetera. Another thing that I believe ties into several of these ideas is the idea of acceptance. Or perhaps it would be better described as a sense of open mindedness, but I will use acceptance for sake of clarification.
It has been mentioned that on earth nowadays we are far form our potential because so many people do not care. They do not care because they do not believe in themselves. The people who have made a difference are people who have accepted themselves (both their powers and limitations), accepted the world (and what impact they have had on it), and accepted their ability to do something about it. Most people do not want to accept responsibility for themselves because they are afraid of facing what they have done (or not done, for some people). One of the first rules for overcoming anything is accepting it, and I think there is an important reason for that.
So, in the Chrono world, what is a big difference between many of the playable characters and villians and the non-playable characters? Acceptance. Chrono and Co and the villians have accepted themselves, their place in the world, and then move on to act upon it.
Take Magus for example. He comes to grips with reality. He accepts that Lavos destroys everything he holds dear, and moves form that to do something about it (first to destroy Lavos, then to find Schala). What about the other Zealians (perhaps the wrong term to use. It is up for debate on another thread)? Some whine about being stuck with the earthbound ones, some hope for a better time, some are gripped with despair, but they have all not accepted the reality of the situation (they still can't believe what has happened to them).
Pierre from Chrono Cross is also similar. He has to accept what it means to be a true hero and his own limitations before he can become that which he truly desires. In fact, I think that is the difference between a lot of the playable and non-playable characters in Chrono Cross, more so than Chrono Trigger.
In any event, I think there is a better word than acceptance, but I am unable to put my finger on it right now. maybe someone else will have an idea of what I am grasping for and be able to enlighten me. Even if I am unable to quite describe it in words, this is what the Chrono feel means to me.
EDIT: Boo's quote caught my grammatical error, so I fixed it. The meaning is still intact.