A fatty acid is a long hydrocarbon chain capped by a carboxyl group (COOH). There are many common fatty acids that you hear about, four of which are shown below along with acetic acid for comparison:
The COOH cap is what makes these molecules acids. You are probably familiar with acetic acid because this is the acid found in vinegar. You can see that the fatty acids are like acetic acid, but they have much longer carbon chains.
To make a normal fat, you take three fatty acids and bond them together with glycerol to form a triglyceride, like this:
Since this particular triglyceride happens to contain three molecules of stearic acid, it is also known as tristearin. This diagram shows one fat molecule. When you eat fat, you are eating collections of molecules like these. The choice of the fatty acids in the fat controls many different things about the fat, including how it looks, whether it is a solid or a liquid at room temperature and how healthy it is for your body. Many of these characteristics have to do with whether a fat is "saturated" or "unsaturated."