The idea behind Mic Drop is simple, and could in fact be useful to some if it were a real feature. Google temporarily added it as a way to effectively end a thread, even if it persists without you. It should be fair to say that most people like to get the "last word" in, and that's exactly what Mic Drop is all about: give your two cents, and then bail out of the thread.
Mic Drop might sound like a fun prank, but when so many people use Gmail for business purposes, it had the potential to put people in a bad spot. After all, a mere message wasn't just sent with Mic Drop – it also included one of those Minions from Despicable Methat the Internet can't seem to get enough of. If you're trying to close a business deal with someone and then received an image of a Minion dropping a mic, that'd introduce all sorts of awkward into the conversation.
To Google's benefit, the company is far from being oblivious to the issues Mic Drop caused, although it's quick to say that business users (through Google Apps) as well as government and educational users never had the feature enabled (which will explain why you didn't see it, if that were the case).
Google raises a couple of points about where it screwed up with Mic Drop. It first points out that it should have raised a prompt when you went to Gmail to explain the feature, and a warning should have been raised if the feature was used. The company also didn't anticipate accidental clicks, and placed the option too close to the "Send" button.
A third point raised is kind of freaky: if you were to open a new compose window, press the Mic Drop option when you had no recipients, and then go back to add recipients, the "Send" button would suddenly act as a Mic Drop button. Ouch!
We think it's safe to say that Google is going to try harder to avoid an April Fools' joke going so wrong in the years ahead. Typically, Google has the kind of April Fools' joke that users actually anticipate, so in a way, it's very unfortunate that its Mic Drop joke didn't go according to plan.