When you step on a specific (cumulative) number of tiles you will unlock various new modes that you will be able to toggle on/off via the 'Options' menu.
Circles Mode (ALL tiles appear as circles instead of squares):
Step on 1,000,000 total tiles.
Convolute Mode (ALL directional input is reversed, even on menus):
Walk off the edge 10,000 times.
Kind Mode (ALL blue tiles are now green):
Step on 420,000 blue tiles.
Nice Mode (gameplay doesn't change noticeably in any way):
Step on 69,000 hard tiles.
Pride Mode (ALL tiles appear in alternating rainbow colours):
Step on 600,000 coloured (non-blue) tiles.