What is the maximum player running speed?

Movement Speed in PlayerUnknown's Battlegrounds is determined by what weapon you are currently holding, as well as your current stance, plus any level 3 or 4 boosts from consumables (Energy Drinks, Pills, Adrenaline).

To break it down fastest to slowest:
Sprinting Player (holstered weapon) with Tier 4 boost = 6.7 m/s (+6.2% speed)
Sprinting Player (holstered weapon) with Tier 3 boost = 6.4 m/s (+2.5% speed)
Base Sprinting Player (holstered weapon) speed = 6.3 m/s

So, at your speediest it will take around 15 seconds to cross one white square (100m) of flat terrain.
So put your gun away and start chugging those pills and energy drinks if you gotta go fast.

(source, all speeds rounded to 2 significant digits)

If you want to run fast, you'll need to holster your weapon (you'll run slightly faster by doing it). On your minimap, you'll notice a grid. At your maximum running speed, you can go through an entire square in approximately 16 seconds (in a straight line from one side to the other).