When I was first studying life in Africa I kept running into accounts of Africans eating "porridge" with "sauce." This was hard to wrap one's mind around, given that "porridge" is oatmeal, a wet gloopy cereal that is close to being a sauce itself. This was the British colonial linguistics in action, applying their term (to be specific, the Scottish term, for a food preparation that led Bobby Burns to wax rhapsodic on "the halesome parritch") to a range of food preparations across Africa that had no direct analog in Europe. Sometimes British writers used the term "dumplings," which is equally misleading. Some early called it "bread," also confusing because the stuff we're talking about isn't baked. Somewhere I saw it referred to as "hand-bread," which is getting closer.
Complicating matters was the fact that Africans themselves had no general term for this form of food -- hardly surprising given the linguistic diversity area across the large area over which it is made. Of its many African names, one of the most widely used is fufu from West and Central Africa, so let's just use that. (Examples of other terms are moen among the Kofyar, ugali in parts of east Africa, and nsima in S. Africa.)
Fufu is a preparation made of boiled starch -- either grain or tuber -- that when ready to eat has a consistency somewhere between very stiff mashed potatoes and play-dough. It is pulled off in chunks and dipped into a "sauce" (or "soup").

To make fufu from a grain, you take the maize / sorghum / rice / pearl millet / finger millet / etc. and grind it into a coarse flour, then mix into boiling water and stir until the consistency is right. There are different procedures for making fufu from a tuber. For cassava, the roots have probably already been grated as part of the detoxification process, so you can go straight to the boiling water step. Yams, the preferred base for fufu in much of West Africa, are prepared by pounding (see yams).
In many places the flour is wetted and fermented for a few days before cooking -- an example would be the Ghanian banku. Other than the fermentation in some cases, there is usually no attempt to flavor the fufu -- there is division of labor with the sauce.
Commercially milled flours of not only grains but also cassava and yam are now widely available. Some purists claim that fufu made from yam flour is inferior in both taste and texture, but they are widely used and most people have made the adjustment. But if you want my opinion, they suck.
Sauce / SoupOnce you have your starchy fufu, the drill is to tear off a small chunk with your fingers, dip in into the sauce, and eat it. The anthropologist on the right is doing this with a cassava fufu, although she wished it were pounded yam which really does have a better flavor. Her dinner was rounded out by a chloroquine tablet and a 16 oz. bottle of Nigerian Star beer.
To understand sauces, you first have to consider the mechanical problem in this approach to dining: if you have a thin sauce, not enough of it will stay on your fufu, and you will basically get a mouthful of starch. There are two different, non-exclusive ways of meeting this challenge: inclusions and thickening.
Inclusions make it so you come away with some flavor and nutrition even if the sauce liquid is thin. Common inclusions are finely chopped vegetables, ground seeds, and leaf vegetables (often shredded). Examples of widely used vegetables are onions, various peppers, tomatoes, okra (more on this one below).
A very common ground seed is egusi (also known as ekwishi, agusi, etc.), which basically means melon -- various species are used. There is a very wide variety of greens used. Leaves of many crops are used, like cassava. Other greens are harvested from the wild, a good example being Gnetum leaves (eru, ukazi), although these are now being cultivated and can be bought in import shops.
There is likewise a wide range of thickeners, both wild and cultivated. Some of the vegetables and inclusions have thickening properties (like okra and egusi), and some ingredients added mainly for thickening also impart distinctive flavors. Okra is an interesting food in this regard. It is an African domesticate brought to the New World along with slave culture, and it still plays a role on southern cuisine. It is a fairly tasty vegetable with an interesting texture, but its sliminess when cooked is a drawback as far as many are concerned. So we make it into de-slimified dished like hot pickled okra . But in African sauces, the gooiness is prized.
The Kofyar used all sorts of thickening agents, including a seed gathered in the bush that when ground made the soup almost too thick, so it was hard to get the glob on your fufu to separate from the bowl. An old man showed me a trick: you hold the fufu in your thumb & first 2 fingers, dip it into the sauce, pull it up, and then use your other 2 fingers like a pair of scissors.