The movement speed is influenced by certain items: boots, pets, capes and archery gear.
Most of these items have a positive modifier, but some (e.g. piglet) have a negative modifier.
Max speed is +60 (higher values are possible but are capped to 60).
The total speed determines the time needed to move from one tile to the next.
The formula deduced from empirical data is:
time needed to move to next tile = 300ms - speed * 2.5ms
For default speed of 0 this means a time of 300ms, for speed +40 this is reduced by 1/3 to 200ms and for max speed of +60 this results in 150ms (meaning +60 speed is twice as fast as default!).