The Special Attack stat of the pokemon using Growth will increase by 1 step (termed BTLs in the Gameboy description) on the Stat growth scale.
Because of the uniformity of the increases of the value, this increase translates into an increase equivalent to half of the original value of the Special Attack stat each time this move is used. In more definite terms, starting with no modifiers, the 1st use of the move will make the Special Attack stat 150% of the original value, the 2nd will make it 200% of the original value, the 3rd will make it 250% of the original value, etc.
Growth will always fail if it has already been used 6 times by the same pokemon, without a move that lowers Special Attack being used on or against the pokemon using Growth. This is due to the fact that a stat may only be raised by a maximum of 6 steps, until it is reset by the use of Haze or the pokemon is switched out normally. The maximum is the limit of how many increases can be applied to a stat. If another move increases the Special Attack stat of the pokemon using Growth, the number of steps that it increases the Special Attack stat by will count toward the 6 step limit, and reduce the number of times that Growth can be used appropriately.
An example of this might be if a pokemon that received a 1 step boost to all stats from the move Ancient Power passed on those increases by using the move Baton Pass. If it is passed to the pokemon that has Growth, that pokemon will only be able to use Growth 5 times before it will fail.