It is obvious that you can perfectly tile floor of a room using square or rhomboid tiles. Similarly it would be easy if we would triangular or hexagonal tiles. Furthermore in all these case we could rotate these patterns by less than 360 degrees and still get valid layouts. Namely you could rotate rhomboid tiles two times, triangles - 3 times, squares - 4 times and hexagons - 6 times. But what about 5 rotations? Or 5-fold symmetry?
More details in a more attractive video form are given in the video by Veritasium, which touches upon fractal created by British mathematician Sir Roger Penrose - Penrose fractal.