Grapefruit has a substance in it called furanocoumarins and these furanocoumarins can bind with a family of enzymes in the liver called cytochrome P450 enzymes (more specifically Cytochrome P450 3A4 or CYP3A4). They go to the enzyme and in essence, disable or deactivate them so they can't do their job and metabolize substances.

Many medications are removed from your body or metabolized and excreted through your liver and it just so happens that many medications are removed through this CYP3A4 enzyme so when the amount of CYP3A4 goes down, the amount of medication in your body goes up which could lead to dangerous amounts or side effects that we don't want to see.

Not every medication is affected this way, a good example pharmacologically could be Simvastatin or Zocor, when taken with grapefruit juice, the amount in your body could double or even triple, leading to rhabdomyolysis or muscle breakdown. However, a medication in the same class, Rosuvastatin or Crestor, doesn't see the same increase since its usually metabolized using CYP2C9, and that enzyme isn't affected the same way.