Back in the day in England, competing fox hunters would toss a stinky fish (possibly a red herring) into the brush to distract their opponent's dogs from the real target: foxes. Similarly, a "red herring" fallacy occurs when someone introduces points that are used to distract from the issue of relevance.
Example: "Officer, why did you pull me over for going 31 MPH in a 25 MPH zone? Aren't there child abusers, murders, and meth dealers that you should be hunting down?"
(This is considered a logical fallacy because, regardless of whatever else is wrong with the world, the arguer was speeding. While the points the speeder makes about abusers, murders, and dealers may, in fact, be true, they are irrelevant to the argument of whether or not the driver was breaking the law by speeding. The officer could just respond with: "Yep, they're out there, and I'm hunting them down, too. Here's your speeding ticket.")
Example: Q: "I think America has kind of lost that American Dream. What can Donald Trump do to kind of bring that back?"
A: "... Look. We will bring the American Dream back. That I will tell you. We're bringing it back. Okay? And I understand what you're saying. And I get that from so many people. 'Is the American Dream dead?' They are asking me the question, 'Is the American Dream dead?' And the American Dream is in trouble. That I can tell you. Okay? He said it's on life support. It's in trouble. But we're going to get it back and do some real jobs. How about that man with that beautiful red hat?! Stand up! Stand up! What a hat! What does that say on it? Wow! Make America great again. That's beautiful. Beautiful!"
(New Hampshire Town Hall, 9/17/2015)
(In Mr. Trump's defense, the question itself is an example of the "Begging the Question" fallacy--it's loaded and clearly identifies the asker's opinion that we no longer have the American Dream. Because Mr. Trump can clearly see the asker's stance, it's difficult to fault him for pandering by reinforcing that person's view. From that perspective, Mr. Trump is committing the Argumentum ad Populum logical fallacy. Additionally, this is also quite possibly the most brazen Red Herring I've ever seen. I have an uncle who, whenever he wants to distract anyone, points toward the horizon and says, "Look at the pink elephant over there." As soon as we turn our heads, we realize we've been had, and we turn back around to hear him snickering as he slips out the door.)