Common term originating in New York that has spread all over the U.S. and canada to discribe making a cold rap verse usually used to discribe rap battles and freestyle. The word has evolved in different cities, in loose your self Eminem states "he's nervous but on the surface he looks common ready to drop bombs"dropping bombs is a synonym of the word dropping rhymes.
To rap about something important, not 'Pussy, Money, Weed.' If a rapper tries to inform his audience about an important topic, he is dropping science. No longer relevant as the act of dropping science ended when people started listening to 50 Cent.
Damnnn Alexandra...dude over there has the hottest tattoo on his arm...it makes me wanna fuck him right now!!"... "Wow girl you're so right...he definitely has some panty dropping ink."
Mentioning that you're wearing an expensive brand of clothing, using an expensive piece of technology, or bragging about other items that you own which are of high value. Brand Dropping is similar to name dropping, the main difference is mentioning merchandise in lieu of a person.
Jon: Dude! Watch it, if you spill that drink on my $ 350 Zegna shirt I'm gonna lose it.
Dave: Stop brand dropping Jon. No one cares what kind of shirt that is.