The term penny shares is most commonly used by tip sheets. It refers to shares that have a low price: a few pence a share as opposed to the more typical tens or hundreds of pence per share.
This idea behind the advocacy of penny shares is that low priced shares have more potential to rise, and therefore investors should do their stock-picking by selecting from among penny shares.
The idea is fundamentally flawed. Looking at price alone, without any indication of what value a share has is not meaningful. A share price can only be said to be too high or low relative to earnings per share, assets per share, or some such similar measure.
It is not possible to say what a share ought to be worth without properly valuing it. Once a real valuation technique has been used, the fact that it is a penny share is irrelevant.
The falsity of the idea that penny share are in some way special is evident if one considers that a company can decide whether its shares are penny shares are not by consolidating or splitting its shares.
There is some evidence that penny shares out-perform, but a close look at the data suggests that this is attributable to other factors: for example penny shares tend to be those of small companies which are known to tend to out-perform for good reasons.
Investors are better off using the more precise technique of screening by market cap to find small companies, and looking at historical data to find recovery stocks.