At its most basic, the TCA cycle is a mechanism which converts the fuel we consume - carbohydrates, fats and proteins - into special molecules called "reduced cofactors" which transport electrons to the inner mitochondrial membrane for use in Oxidative Phosphorylation.
However, in reality the TCA cycle is probably the most important metabolic pathway in the human body. It acts as the major molecular crossroads, where the body can ensure that there are sufficient levels of glucose and protein for normal function, and store any excess fuel as fat. This is why sugary drinks have been linked to obesity - the sugar gets converted to fat in the TCA cycle.