Insight was the power to see parallel dimensions and realities simultaneously with your own. It could therefore be used to foresee the possible outcomes of any given situation. Without proper training, it would turn the user mad.
Samantha famously collected Insight and used it as a form of currency.
The God of Time most likely relies partly on Insight to predict the different outcomes of events.
Titanus was driven to madness by it.
The Hat continually supplied its user with Insight.