In both Mario Kart: Double Dash!!, Mario Kart Wii and Mario Kart 8 acceleration is a relative stat: it measure how fast your relative speed (actual speed/maximum speed) increases. You can see what this means in those videos:
This video shows that in MKDD two karts having the same acceleration parameters but different speed have different absolute acceleration.
Although the purpose of this video is different, you can clearly see that in MK8 combination having different (Land) Speed values with the same Acceleration value have different absolute acceleration.
In Mario Kart: Double Dash!! acceleration is probably governed by 5 values (plus 2 values related to the drifting condition), but only two vary depending on the kart chosen, that are reported in the table of the stats as "first parameter" and "second parameter". The first parameter is the first acceleration-related value in the raw in-game data and it apparently determines acceleration from a standstill until a set threshold speed (should be 15 km/h, the speed at which you can start drifting) is reached, while the second parameter is the fifth acceleration value and determines acceleration once a threshold speed of around 40 km/h is reached:
An acceleration test. You can see combinations that share either the first or the second acceleration parameter here
A neat test. Both karts share the same first parameter and their maximum speed differs only by 1 unit, so they start with a very similar acceleration, but once the threshold speed is reached the Toad Kart, with its second acceleration parameter of 0.01 instead of 0.005, has way higher acceleration.
Acceleration itself, in the parts where the parameter remains unchanged, follows a shape similar to the generalised logistic function, with it being slower at the beginning and near maximum speed.
Mario Kart Wii uses different set of parameters but the same principles. There should be threshold speeds (relative speed in this case, so something like 55% of maximum speed and so on), that determine the stage of acceleration and thus what S value is governing acceleration. It seems that the same values governing acceleration seen in Double Dash!! can be obtained by multiplying S by E, so for example, the equivalent of Double Dash!! first parameter is S1 X E, while the equivalent of the second parameter is S4 X E.
Now, we are still waiting for the actual in-game parameters of MK8 to be revealed, but test done on acceleration tiers suggest that an acceleration system akin to that of MKW might still be in MK8, with the subtiers changing the S values, while the E value is changed when the tier changes. So, for example, in 200cc going from 3.5 to 3.75 acceleration increases only the S values by little, while going from 3.5 to 4 increases both the S values and the E value, resulting in the stark difference observed.
