Acceleration is a statistic in every single Mario Kart and was first only measured on Karts, but on later titles, it also is a stat on Bikes, ATVs, Wheels, and Gliders . It measures how fast the vehicle will achieve its maximum speed, and also how well a vehicle will recover its speed when stopped or slowed down by an Item. Generally, heavy vehicles have low acceleration stats but are very fast when they get going, and light vehicles have low maximum speeds but accelerate quickly due to low Weight stats.
In Mario Kart 7, the acceleration stat is determined by the value shown on the acceleration stat bar. If three sections are blue, then the acceleration stat value is 3 points. If three and a half sections are blue, the value is instead 3.5 points.
The acceleration stat determines acceleration tier the player is in is determined by the value shown on the acceleration stat bar. If the stat value is 2.75-3.5 points, the player is in the 3rd acceleration tier. If it is within 3.75-4.5 points, the player is within the 4th tier.
However, there is an glitch with how Mario Kart 7 handles the acceleration stat that causes players with more than 4.75 points in the stat to accelerate faster than they are supposed to. This glitched increase in acceleration with the stat above 4.75 points is known as the acceleration glitch.
In Mario Kart 8, the acceleration tier the player is in is the same as the amount of full bars on the acceleration stat (or the acceleration number rounded down). The acceleration tier glitch from Mario Kart 7 is fixed as there is no increase in acceleration with a stat higher than 5 points.