These are the Vibram Furoshiki wrap-around shoes. They were inspired by traditional Japanese Furoshiki fabrics used to wrap gifts or transport goods. They're basically a rubber soled slipper with a long piece of fabric on each side that wrap across the top of your foot and are secured with Velcro. They are perfect for people who are too inept to tie their own shoes, but are afraid people will make fun of them for wearing regular Velcro straps. These are like a compromise, because there's still the possibility you'll wrap the straps UNDER your foot and get made fun of in gym class. Afterwards, all the boys in the locker room will make fun of you for the poop-stain on your underwear, and you will have no choice but to call your parents and beg them to let you transfer colleges.
Keep going for a bunch more shots and a video.
Thanks to Tamiana, who agrees the real future are shoes that stay on with suction cups.