Going by the name "urea breath test," this isn't so much a test as what doctors call the least-popular resident in med school. And just as a bonus, there's radiation involved! Find out why you would be forced to endure this medical procedure.
Chemists are not interested in euphemisms. When they discovered a major component of urine, they went ahead and gave it a name to let everyone know exactly where it comes from. And then doctors took it one step further and made you swallow it so they can detect pee digestion on your breath.
To be fair, the urea in the "urea breath test," is not coming out of another person's body. In the body, ingested proteins are slowly broken down into amino acids, and those amino acids are further broken down in the liver to ammonia, carbon dioxide, and water. Ammonia should not be inside the body. To keep the ammonia from doing damage in its natural, NH3 form, it gets a nitrogen atom, a hydrogen atom, a carbon atom, and an oxygen atom added on to it. The resulting compound, known as urea or CH4N2O, is a white powder when solid, travels harmlessly through the body in the blood. The kidneys filter it out of the blood and store it in the bladder, and from there it's generally excreted a bathroom or a suitably dark alleyway - whichever is closer.
Soon, though, there wasn't enough pee in the world to satisfy the need for urea. It's in resins and fertilizers, and kept in big jars in biochemistry labs, ready for all kinds of experiments. Today it is manufactured in labs by combining ammonia and carbon dioxide at high pressure. The ability to manufacture it comes in handy for doctors, who add a little radioactive carbon-14 to the mix. They then make a person swallow down the newly-made urea and start checking their breath. If the patient starts exhaling carbon dioxide tagged with the carbon-14 in the next few minutes, the doctors know that the urea is being split apart.
Due to medical consent laws, which prevent doctors from making patients swallow urine components for fun, there needed to be a reason to make the patient take the urea. Fortunately, the doctors managed to hit upon a neat little test to justify their prank. In 1982 researchers learned that the bacteria helicobacter pylori caused chronic ulcers. Although the bacteria present in most people's digestive system, when it gets out of hand it causes terrible pain and indigestion. Part of h. pylori's biology is a little enzyme called urease. This enzyme splits urea in two. Nothing else in the body would break up the urea so quickly after it is swallowed, so the presence of tagged carbon dioxide in the breath allows doctors to find out if the person with stomach pains has an overabundance of this bacteria in their system.