The Defense stat of the pokemon using Harden 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 Defense stat each time this move is used. In more definite terms, starting with no modifiers, the 1st use of the move will make the Defense 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.
Harden will always fail if it has already been used 6 times by the same pokemon, without a move that lowers Defense being used on or against the pokemon using Harden. 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 Defense stat of the pokemon using Harden, the number of steps that it increases the Defense stat by will count toward the 6 step limit, and reduce the number of times that Harden can be used appropriately.
An example of this last part might be if another pokemon who has both Defense Curl and Baton Pass used Baton Pass after using Defense Curl 3 times. If another pokemon that has Harden is the receipient of the Baton Pass, it will only be able to use Harden 3 more times before the move will fail.