These aren't brightly lit clouds. They're mirages, just like the mirages you see on the roads on hot days. Air bends light differently depending on what temperature it is, and the hot air rising from a road can bend light coming in from the sky - or from distant objects - back up so that it hits your eye. You see blue or dark patches in the middle of a light gray road. The same happens with the sun. Layers of hot or cool air can run for miles over the ocean, and they bend sunlight streaming upwards towards the upper atmosphere back down so it can be seen by people watching the sun set.
The Novaya Zemlya Effect gets its name from the island off the coast of Siberia, where it befuddled the crew of a Dutch exploring expedition. Being sailors in the late 1500s, they took celestial objects and time keeping very seriously - knowing where heavenly objects were meant knowing where they themselves were. And so it bothered them when sunrise regularly came earlier than they were expecting, and sunset came later. It wasn't until the sun started coming up square, or sometimes coming up in segments across the sky, that they realized what was happening. The mirage was so intense that the sun appeared to be rising minutes earlier than it actually did rise. They named the effect after the island, and the name stuck.
All I can think of are all those old vampire movies, where the vampire is about to strike - only to be chased away by the first rays of the sun. Around the poles, when dawn can come even earlier than expected, it had to be tough to be a vampire. You'd have to build in extra time to get anything done.
Arctic sunrise image via Martin Lopatka/Flickr. Mirage image via Brocken In A Glory