Moral foundations theory is a descriptive theory about human psychology, backed by research, which has tried to identify some of the main forms of thinking which underlie people's moral beliefs. People evolved with tendencies to think about moral topics in certain ways, including not just in their explicit reasoning but in their emotions and implicit theories. For instance, people often apply a purity/contamination model to social & moral subject matter, which is facilitated by the emotion of disgust. Different cultures build different sets of moral views out of these building blocks. For example, different cultures have different views about what must be kept pure (and from what potential contaminants, and how, and whether/how it can be re-purified, etc.). Most cultures make use of all of the moral foundations, but WEIRD cultures (including American liberals and libertarians) draw primarily from a limited set of these foundations. That's the descriptive side, his moral/political psychology.

The prescriptive side: Once you understand the descriptive side, it seems like that will have some implications for moral/political philosophy. How humans think about morality and social/political issues is probably relevant to how to create a thriving society of humans. In Haidt's case, he started as a fairly standard American liberal and found that his psychology research led him to become more receptive to some conservative/traditionalist arguments, and to identify some things which he believes that traditionalist societies have gotten right (and which liberals tend to get wrong). He thinks that many liberals have the blind spots that he used to have, and that learning moral foundations theory would help them to reach similar insights about how to build a thriving society.

Haidt makes some efforts to keep these two sides separate, and generally does a better job of it in his own writings than he does in other media. I recommend trying to focus on the descriptive side first.