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.