This is a combination watch / vortex manipulator, worn by the character jack harkness: http://tardis.wikia.com/wiki/Jack_Harkness
Its main use was to teleport the wearer through time and space (although this one just lights up). This uses a very similar battery and led to my sonic 'ible: https://www.instructables.com/id/how-to-make-a-simple-sonic-screwdriver/
. the band is leather, with a button holding the flap down. On the inside the watch face is just a boring old digital watch. then you'll want to cut some thin wood for the top to fit around the watch and led.
If you have any questions or pics of your own, post them in the comments below.