Actually, "counterfeit medicine" is a euphemism for "generic drugs", i.e. drugs that have been manufactured and sold without paying the patent owners anything.
Some drugs (especially for various types of cancer) cost more than $100,000 per treatment and some third-world countries produce their own local "generic" version of the drug, since they can't afford paying that much for saving just one life. The production costs for a drug sold for a six-figure sum are typically under $100.
The "big pharma" try to prevent poor consumers from first-world countries from traveling to third-world countries and buy these drugs, this is all there is to it.