A champion’s speed is determined by their movement speed. Now, some champions may have high movement speed by default, but that only helps them at the start of the game. As other champions unlock abilities and get items, they gradually increase their individual movement speed.
For example, a level 6 Miss Fortune with boots will be faster than a level 1 Master Yi with no items. This is because Miss Fortune will not only have the speed increase from the boots, but also her ability that increases her movement speed. There are naturally many ways to increase movement speed, and some champions like Zilean can also increase or reduce the movement speed of other champions.
What some champions may not know is that the terrain can also impact how fast a champion moves around the map. This is thanks to abilities like the ones Talon and Kayn possess which allow them to go above or through walls to quickly chase or escape from enemies.
Alternatively, there are also things like Hextech Gates and explosives that can help players move from point A to point B quicker than they could by walking.