Acid growth refers to the ability of plant cells and plant cell walls to elongate or expand quickly at low (acidic) pH.
The cell wall needs to be modified in order to maintain the turgor pressure.
[1] This form of growth does not involve an increase in cell number.
A typical sequence leading up to this would involve the introduction of a plant hormone (auxin, for example) that causes protons (H+ ions) to be pumped out of the cell into the cell wall.
It was suggested by different scientist that the epidermis is a unique target of the auxin but this theory has been disapproved over time.