A moral economy is one that is based on the goodness and fairness of the people participating in it. Such an economy generally only works with small groups of people who know each other fairly well and who aren't likely to try to cheat each other.

Moral economies tend to be "scratch my back and I'll scratch yours" type of arrangements. They prevent free rider problems by leveraging the willingness of people to help others and generally follow the rules.

Joseph Heath's The Efficient Society provides an entire chapter on the moral economy, and he does a much better job of explaining it than I can.