This is the iPhone-Version of the Chromachron watch, designed in the 1970s by Swiss designer Tian Harlan.
The color circle represents the course of the day by light and color degrees.
Telling the time with it is basically pretty easy. Imagine having only an hour-hand on your watch. The hour hand of the chromachron is the black disk with the cutout.
Every color represents an hour – whereas yellow is 12 o clock, orange is one and so forth. If you can see the entire color piece in the discs cutout, the hour is «full» - if you can see half of a color its «half» the hour. E.g. if you can see half of the orange color its 12:30 (half of 1). If you can see 3/4 of orange, its a quarter to 1 (3/4 of the first hour)...
With a little practice, youll be able to tell the time with an accuracy of about 3-5 minutes. Not exact? Well, thats the point :) By using the Chromachron watch, youll be less stressed, because its always «about... 5:30».
There are still Chromachrons available. Used ones can be found on eBay. Theres also a company that sells new ones (decide for yourself whether you like them).