How big is a tile?

Short answer: The tiles are about a mile square.

The most zoomed in tiles that are used on this site (and are recorded on VeloViewer) are the "level 14" tiles from the OpenStreetMap. To get to level 14, you start at level 0 which is one single tile representing the whole world. You then zoom in to split that tileĀ into 4 equal-sized tiles, each with a side half the length of the first tile. This gets you level 1. Then you zoom in again splitting those four tiles into four tiles each, making a total of 16 tiles covering the whole world at level 2, each with a length of a quarter of the length of the original. So at level 2 you have a total of 4*4 = 16 tiles.

Do this splitting procedure 12 more times and you get to level 14. So there are 214*214 tiles covering the Earth. That is 268,435,456 tiles! The length of the tile is halved each time we zoom in a level. This means, at the equator, the size of a tile S = (circumference of the earth)/214 But I don't ride at the equator, as we get further away from there, the tiles get smaller as they head towards the North Pole, where they vanish to nothing. In fact to get the formula for the width of the tile we need to think back to our childhood trigonometry lessons: I live at 51.5 degrees North so, for me, the formula is

Size = Circumference of Earth * cos(latitude) / 2^14
     = 40,075km * cos(51.5 degrees) / 16,384
     = 1.523km
     = 0.95 miles.
But it's best just to say "about a mile".

OpenStreetMap has a page all about zoom levels.