What is intuitive eating?

Intuitive eating is a philosophy of eating which is based on the belief that the vast majority of people are born with all of the intuitive wisdom they need to have to know how to eat.  That includes knowing when they're hungry and full, knowing what taste preferences they have, and knowing how their bodies feel after making their food choices.  Unfortunately, many people, for various reasons, become distracted from this wisdom.   These people need to challenge their diet thinking and distorted cognitions and myths in order to find their way back to their inborn wisdom.

What are its origins and how big is it as a worldwide movement?

The origins of Intuitive Eating come from a movement toward a non-diet philosophy which emerged sometime during the late 1980's.  It became evident that dieting for the purpose of weight loss could only lead to failure, more weight gain, and lowered self esteem.   The two authors of Intuitive Eating, both Registered Dietitians were the first dietitians to take this broad philosophy and lay down ten principles, named the principles of Intuitive Eating, which addressed how people could move away from diet thinking and move back toward their intuitive wisdom about eating.  The original edition of Intuitive Eating was released in 1995, with a second edition in 2003, an audio book with guided practices for all of the Intuitive Eating principles in 2009, and now the 3rd edition in 2012.  The term, "intuitive Eating" was coined by the authors.

Why is it a better option than three meals a day and other more structured eating philosophies?

A structured meal plan or diet comes from "the outside in" rather than "the inside out".  In other words, structured plans tell people what to eat, when to eat, and how much to eat.   This is completely counter to and invasive of the very private place within each human that houses the information responding to the what, when, and how much to eat.   Diets engender deprivation, with its accompanying deprivation backlash and rebellion against being told what to do, which triggers an individual's need to assert autonomy by going against the diet.   Dieting has been proven to be a consistent predictor of weight gain.