1. Sitting on a toilet and unloading fecal matter into the bowl.
2. Using the restroom (#2).
The term "platinum" derives from an urban clothing line "FUBU". The name itself sounds like something that comes out of your ass (feces). FUBU then upgraded their clothing line to "Platinum FUBU". Hence, an upgraded shit. So, when you drop platinum you are unloading something really nasty. The term became, "dropping platinum fubu". It was too long to say, so it got shortened to "dropping platinum".
"Hold up, I gotta drop platinum."
"Wassup, what you up to?"
"Chillin, droppin platinum"