From The New York Times:
Q. So what exactly did you find on this unexpected road?
A. As we did our research, you could see there was a big difference in the way monolingual and bilingual children processed language. We found that if you gave 5- and 6-year-olds language problems to solve, monolingual and bilingual children knew, pretty much, the same amount of language. But on one question, there was a difference. We asked all the children if a certain illogical sentence was grammatically correct: “Apples grow on noses.” The monolingual children couldn’t answer. They’d say, “That’s silly” and they’d stall. But the bilingual children would say, in their own words, “It’s silly, but it’s grammatically correct.” The bilinguals, we found, manifested a cognitive system with the ability to attend to important information and ignore the less important.
Q. How does this work — do you understand it?
A. Yes. There’s a system in your brain, the executive control system. It’s a general manager. Its job is to keep you focused on what is relevant, while ignoring distractions. It’s what makes it possible for you to hold two different things in your mind at one time and switch between them. If you have two languages and you use them regularly, the way the brain’s networks work is that every time you speak, both languages pop up and the executive control system has to sort through everything and attend to what’s relevant in the moment. Therefore the bilinguals use that system more, and it’s that regular use that makes that system more efficient.
More here.