Wikipedia explains that grapefruit juice is plentiful with vitamin C, but is also a potent inhibitor of the cytochrome P450 CYP3A4 enzyme.
Wikipedia further explains that cytochrome P450 CYP3A4 is the most important enzyme for metabolizing xenobiotics. These are chemicals that are found in an organism that are not naturally there or part of its diet. Say for example, a pharmaceutical drug that you are taking for some reason or another. That would be a xenobiotic.
Grapefruit Juice and Medicine May Not Mix explains that CYP3A4 breaks down xenobiotics such as drugs in the small intestine. But grapefruit juice inhibits the metabolism of the drug, so it stays in the bloodstream longer than it should. Drugs that are particularly dangerous with grapefruit juice in your body include statins such as Lipitor and blood-pressure lowering drugs such as Nifediac. People have differing levels of CYP3A4 in their small intestine, so it is difficult to predict an individual's reaction to the mixing of grapefruit juice and a drug.
Not mentioned by the FDA, but cautioned by Wikipedia include drugs such as oxycodone.
Curiously there are other drugs affected by grapefruit juice that have an opposite reaction - the juice retards absorption of the drug. For example, Allegra is not absorbed by the body due to grapefruit juice blocking the transport of the drug instead affecting metabolism.
The FDA recommends that you specifically ask your doctor or pharmacist about interactions with any fruit juices in your diet and your medication. The FDA requires this information when a company applies for approval of a new medicine.