By averaging down the investor gets more share per dollar.
The effect of such purchases is that they bring the average price of the purchased shares down, closer to existing low level prices, rather than the previous higher costs.
Averaging down can cover for losses, by bringing the price sufficiently low to make the said shares interesting enough to be bought and thus, hopefully, creating some gains. This improves the chances that the stock will become profitable and can lead to speeding up a potential break-even on the investment.
Furthermore, if the price of the said stock increases after the transactions, the investor will have made a profit. On the other hand, there is the risk that the price will continue to fall, in which case averaging down could generate losses.
This type of investment operates on the assumption that the price of the said shares will increase. As such, it can be risky to decide when to average down. Buying when share price is falling is not difficult, but one must have considerable confidence that the stock invested in will rebound high enough to top the average price per share.