A "wedgie" is when someone grabs your underwear and pulls it up! The "business end" of something is the area where the main work is being done. So, being on the "business end of a wedgie" would mean you are the one whose underwear is being pulled! The phrase "business end of a wedgie" is usually used metaphorically, referring to someone being treated lesser or being on the lesser side of an interaction, transaction, etc. Of course, in the unfortunate case of a real wedgie, it would obviously work as well! ;P

To be on the business end of something means you feel the effect of it, and a wedgie is something schoolchildren do to each other: one person grabs the other's underpants and pulls them up sharply causing pain, discomfort and embarrassment. So the phrase as a whole means "becoming the victim of a mean, underwear-based prank"