Healthy sleep puts us in the right state of mind to take in information as we go about the day. Not only that, we need a good night's sleep to process and retain that information over the long term. Sleep actually triggers changes in the brain that solidify memories—strengthening connections between brain cells and transferring information from one brain region to another.
Researchers have tested this process by teaching people new skills and then scanning their brains after a period with or without sleep. When people have a chance to sleep, for example, after practicing a skill similar to piano scales, the centers of the brain that control speed and accuracy are more active than those regions in people who haven't slept. Scientists think that while we sleep, memories and skills are shifted to more efficient and permanent brain regions, making for higher proficiency the next day. In fact, sleeping shortly after learning new information has been shown to help retention. Some research indicates that when people learn before going to sleep (or even before taking a nap), they remember the information better in the long term.
Sleep also helps us synthesize new ideas, not just remember the old ones. While you're sleeping, pieces of knowledge can be pulled together from different experiences and parts of the brain to create novel concepts or "ah ha" moments. That's a big help when you're trying to solve a problem or make an advance in your work.
In a new twist to the story of sleep and learning, researchers have seen that we may actually be able to learn new information while we sleep. To test this idea, scientists exposed people to a sound and a pleasant smell while they slept. After the subjects woke up in the morning, they started sniffing when they heard the sound (even though it wasn't followed by a smell). In other words, they had learned the association while they slept.
The science of sleep and learning continues to grow, but it's clear that the brain needs adequate sleep to sort through our experiences, so that we can remember and function at our best and most creative the next day.