I read a very interesting New York Times article about the psychology of wisdom. As writer Stephen Hall re-iterates, wisdom is a very fuzzy topic. There are apparently as many as 13 definitions of wisdom. Hall discusses at least two definitions. One definition is practical experience and problem solving as applied to major life decisions/crises. Another definition is emotionally based. According to this definition, some examples of wisdom are emotional detachment (being "even keeled"), resilience in the face of adversity, and compassion/perspective for other people.
I'd like to propose a physicist-inspired definition. I think wisdom is the ability to identify and apply the right time-scale and person-scale to the problem. Time-scale wisdom is the art of recognizing whether information is important that you should act on it now or just let it go. I'll try to make this statement more clear. For example, it's very tricky for parents to deal with the emotions of a teenager. There are some experiences that are just normal to growing up (failing a test, breaking up with a friend, etc) and a parent should let things be. But there may be instances where a parent would want to stop their teenager from going off on a bad trajectory (for example, going camping overnight with sketchy boys). I don't have very much person-scale wisdom or a good feel for it, but my best definition is knowing who are the relevant parties. Is this a situation where your action will affect multiple people? You might even be able to divide up a person (an even smaller scale) since a person will often have a personality with many conflicting parts. As all physicists know, often the first step to solving a problem is to figure out the relevant time and spatial scales. You don't need quantum mechanics to understand the dynamics of a macroscopic pendulum.
I also like how the article points out that "the old are not always wise and the young are not always lacking in wisdom." There is a tendency in some culture to revere elders and use that as an excuse to abuse the younger generation. I think it's a good thing to respect your elders and listen to them most of the time, but like all things, there is a balance.