Incubate

If you let an idea stew on its own while you've stepped away, it's usually suddenly much clearer when you come back. The odd shapes in the picture suddenly look like something real, the darker parts have adjusted to your eyes, and everything finally seems to fit together.

This is the second phase of creativity: preparation, incubation, illumination, and verification. You start out by assessing the problem and gathering information. Then, during incubation, the brain subconsciously processes the information even though you're not actively thinking about it. The thought then reappears into conscious awareness, and finally you validate and verify.

This 4-stage model was presented by Wallas in 1926, but how the incubation phase actually works is still an open question. It's been suggested that the break from conscious thought allows us return to the problem with fresh eyes so that we can restart from being fixated on the wrong perspective. The alternative process is that leaving a task knowing you will come back to it allows the brain to work on it subconsciously in the meantime [1]. In either case, the effect has been happily experimentally noted many, many times. Like Don Draper says to Peggy in Mad Men, "Just think about it. Deeply. Then forget it, and an idea will jump up in your face".

[1] Creative People Use Nonconscious Processes to Their Advantage