Can anyone shed light on this "fast" term that's tossed around?
To me, "fast" may mean a couple different things.
Obviously, one is "athletically fast" - a bunch of guys who are physically capable of flying around and making plays, even in situations that they may have misjudged at the snap (make-up speed). A defense that's fast based primarily on the athleticism of it players may get "gassed" in a longer, hard-fought game if the teams doesn't have enough viable rotational subs, and/or if the conditioning of the players isn't top notch, and/or if the players don't know how to properly pace themselves.
Then there's "anticipation fast". I just made that term up, so there's almost certainly a better one.
What I mean is a defense that may be not so athletically gifted, but is physically well-conditioned, deep (in the sense that there's not an enormous dropoff between the #1s and their rotational/situational subs), very good at correctly diagnosing plays, and very well-trained in their assignments. Early and accurate reads of what the offense is attempting to do, and fewer false steps means a defense that "plays fast", even if the players aren't moving at light-speed.
One of the things I loved about watching Junior Seau in his twilight years with the Pats (well after he'd lost most of his athletic speed) was that he never seemed to be in any particular hurry, and yet he nearly always ended up in the right spot to make the play. He'd seen pretty much every play disguise an offense could throw at him, so his diagnosis was instantaneous. It's like he knew where everybody would end p before it happened. I saw running plays where, after the ball was snapped, Seau would seem to casually stroll over to a spot and just wait for the RB to run right into his open arms. That's "playing fast" without moving fast.
The relevance to this "new Flores defense" is that, there's a popular hypothesis, based primarily on comments by HT, that the defense will "play faster" this season because Flores has made their assignments (how to read and react to specific play scenarios) easier to understand and remember. Fewer "options" to think through = fewer false steps and mistakes.
I think this is probably true.