How is this possible?
I’ve described this effect before. Video is an illusion; it’s really a series of still images that are shown so rapidly our eyes and brain interpret them as continuous motion. If you can time some sort of motion correctly, you can trick the camera (and the viewer) into seeing motion that isn’t really there. It’s why you sometimes see car wheels apparently spinning backwards in TV shows. Really the wheel is making almost one complete turn between video frames, so when you play the video back it looks like the wheel is rotating the wrong way.
In the case of eggs, patterns are drawn on the eggshell such that spinning the egg causes the same sort of beating with the video frame rate. A simple case would be to draw a series of dots around an egg forming a tilted circle around it. If you spin the egg such that the next dot comes into view just as the camera takes a video frame, it’ll appear that the dot moves up and down. With time.
In the video the patterns are substantially more complicated, but the principle is the same. They were drawn using Egg-Bot, an open-source art robot, which you can buy at that link (and the Electro-Kista, which you can also get online). Very cool.
Of course, you can also decorate eggs in a new version of the old-fashioned way like my friend Jenny did. That’s cool too. Either way, you have a year* to think about it.
*Correction, March 28, 2016: I originally wrote "you have 364 days," but Easter doesn't happen on the same calendar date every year. It'll be on April 16 in 2017.