Name dropping is mentioning someone important so others will like you. Often but not always untrue. For instance, Fred is name dropping in the following example:

Fred: I was hanging out with Puff Daddy . . . do you know Puffy?
Barney: No, is that some guy you slept with?

In a conversation, the act of referring to something for the sole purpose of implying to everyone that you know of or like said object.

Alternatively, especially in music, film, or other modern arts, it is the use of totally unknown names to imply (whether intentionally or not) that others involved in the conversation are simply not as informed or up-to-date in the field as is the speaker. The speaker gains a feeling of superiority and confidence from this in a conversation, which is no doubt part of the perpetuation of the concept of being "underground" or "indie".

This is perhaps the driving force behind indie rock, which consists largely of a multitude of bands that sound remarkably like one another and are generally very musically generic, but which maintain popularity by appealing to people who will alter their tastes to suit whatever new no-name CD they forked over $10 for at their local college music retailer at the recommendation of their more musically competent friend.