TCA stands for tricarboxylic acid and is the name of this cycle of reactions because the first product of the cycle is something called citrate (or citric acid) - which is a tricarboxylic acid. Other names for the cycle are the Kreb's Cycle and the citric acid cycle - again because it starts off with this citrate molecule being produced. It is a really important part of metabolism because the products of both glycolysis and the beta oxidation cycle are acetyl CoA, which is needed in the first step. The series of reactions go round and round again - the core structure (e.g. oxaloacetate) just goes round and round; it's things like the acetyl CoA which need to come in. The reason we break down glucose and fats isn't to produce oxaloacetate; it's to provide the acetyl CoA so that the cycle can keep going. The cycle produces molecules of NADH and FADH2, so that energy can be 'produced'.
Adding acetyl CoA to oxaloacetate means that the oxalacetate ends up with an extra two carbon atoms in its carbon skeleton. These two will be lost during the course of the next few reactions. The CoA is lost in this first step, and can be used somewhere else - it's always very handy!
An enzyme helps to swap around some of the atoms in the citrate molecule to make it easier to use for the next step.
When NAD+ comes along and takes a couple of hydrogens, a molecule of carbon dioxide is lost from the basic molecule. This leaves something called oxoglutarate - which importantly now has only 5 carbon atoms in it.
When another NAD+ comes along with a molecule of conenzyme A, the oxoglutarate looses yet another carbon atom in the form of carbon dioxide, and the CoA sticks on, producing something called succinyl CoA. The NAD+, as always, goes off with a hydrogen.
Converting succinyl CoA into succinate gets rid of the CoA, and also produces GTP (storing energy much like ATP, but with guanine instead of adenine).
When FAD grabs another couple of hydrogens, a double bond is formed in the succinate molecule forming fumarate.
Adding water gets rid of this double bond, and produces something called malate.
And finally, to bring us back to the start, another FAD grabs another couple of hydrogen atoms off the malate molecule, giving us oxaloacetate. This means that oxaloacetate can go back into the start of the cycle and citrate synthase can do its job, producing citrate, which then produces isocitrate, and so and and so on....
This cycle can go round and round, provided that there is some acetyl CoA to come into the reaction - which is obtained, as previously mentioned, from glycolysis or fatty acid metabolism. And so from these reactions we produce FADH2 and NADH, which go through a complicated process called oxidative phosphorylation. This process produces ATP, which is effectively like an energy store - and therefore this whole process effectively generates energy! Marvellous!