I'm going to describe what I think it the full Monty of wisdom, but even if a person only has part of this, they can be wiser than the average bear. Some of this comes from what Judaism has taught me, and some of it is from my own personal pondering on the matter throughout my life. I am also indebted to:
I believe that at the heart of the matter are experiences that feed wisdom. It is very difficult to describe these "religious" or "mystical" experiences. They can't be forced, you can't hang on to them, you can't really put them into words... But you can't escape the feeling that you learned something important. It's like a HINT of something profound that you can't quite put your finger on. It is as if you have been touched by God.
For the wise person, it gets translated into a natural walk of righteousness, of knowing right from wrong, of loving one's neighbor as one's self. There is an ease, a naturalness to it for the wise person... It is as effortless for such a person to act with kindness as it is for them to read a book or shoot hoops or sing a song or whatever their hobby may be. For them, the way of virtue flows like water running downhill because it is sustained by these experiences.
But they are not content to settle for this innate morality. They study to improve their moral and spiritual understanding. They read the sacred texts and the sages. They spend time mulling over moral dilemmas, trying to figure out how to apply the principals and rules they have learned. They believe that God loves them as they are, but also that he calls them to something ever higher.
Another element of their wisdom is the worship and appreciation of the Divine. They know their place in the universe. They care for what is beneath them, and exalt the Creator above them.
However, they are well rounded. Their lives are not dominated by right action, study, and worship alone.
For example, knowing how brutal life can be, they savor every joy that comes their way, no matter how small. Indeed, they have learned to enjoy the boring times, because that means that no negative drama is going on! I call this an attitude of gratitude -- the ability to enjoy the simple beauty of the sun shining in through a window.
They are hopeful, but it is a realistic sort of hope that is conscious of the complexities of life.
They are aware how truly difficult it is to change people's minds, and therefore how high the cost is of being too frank. They put a premium on getting along, and therefore tend to be very polite. They have the capacity to sit with someone with an opposing view and not feel the need to convert them. And they have the capacity to see things through the eyes of the other person.
The wise person draws a very small circle of what they actually need, which makes them much more resilient and far less anxious and depressed when things that are helpful but not actually needed are taken away.
They are deeply aware how foolish human beings can be, and are never surprised by it. They know how to laugh at themselves.
They've come to accept themselves for who they are with all their warts. They also are realistic about others. Knowing the sort of pressures that come to bear on us all, the wise are slow to anger and judge, and have a much easier time forgiving.
The wise realize that it is impossible to go through life without making at least a few incredibly stupid mistakes. They don't waste time in undo regret.