This is a binary pocket watch, made with an atmega48pa. The enclosure is from a cheap pocket watch, mass produced in China and sold via Ebay or Aliexpress.
Open the watch. The upper four LEDs show the hours in binary, the lower six ones show the minutes. Add the numbers under/over the glowing LEDs to get the current time. Closing the watch will turn the LEDs off again.
Press the button for at least 4 seconds (this is called a long press). After release the hour LEDs are blinking. Pressing the button for a short time will advance the hours. Another long press will enable you to set the minutes in the same way. Pressing the button for a long time in minute setting mode or closing the lid will reset the watch to count and show the time again.
Have a look at the construction manual if you want to build your own.