So far as I understand it, Penny Stocks are effectively very cheap stocks - literally, often only costing pennies, at under $1.
Problem is, these stocks tend to be very high risk - issued by high risk and small businesses, where long-term value may not be great.
However, with all risks, it seems the bigger the risk the bigger the rewards - if you get it right.
Another point about Penny Stocks is that they tend not to be listed on exchanges, but can simply be traded "over the counter" between brokers and even customers directly.
Hope that helps.