Project based learning is where the class is taught with a more "hands-on" approach. You explore real-world problems and challenges instead of just focusing on information in a textbook. Basically, regular learning is theory, project based provides actual experience.
For example, in my Marketing course, instead of just learning from the textbook how company's market their products, we were assigned a major project in which we had to pick a product, develop the marketing and explore reasons why the marking we chose would actually be successful. We had to research the law and regulations that governed the region we would market in, any laws or regulations that governed the specific product, stastical data about the market and product, etc. Every concept of marketing was incorporated into the project, week by week. To be honest, it made the course much more interesting and easier to comprehend because we weren't just reading the dry textbook.
As far as a shy kid doing well in an LAC....it really is going to depend on the level of shyness and the willingness of the kid to break out of their shell. Some kids are too content with their shyness and will not excel at an LAC, while others learn to quickly overcome their shyness and excel within a short period of time.