This is actually the meaning of "pace", or "tempo" as my high school coach put it. And it's completely mental. You use ball movement, spacing, and court vision to put the ball in a place where the defense can't easily react or rotate. It makes it seem like you're a "running" team cause the defense is always on their heels, and yes, you do look to push the ball when necessary... but you're not a "running" team. That's not what defines you. What defines you is being mentally sharp and quick and crisp. This will lead to open shots, and defenders being even just slightly out of position, or shading the wrong way.
Coach K uses shot clock drills (12 seconds for example) not for the purpose of getting a shot off fast, but for the purpose of eliminating mental lapses in an offensive possession. Coach K probably believes that a well run offense SHOULD be able to get a good shot within 12-15 seconds. It creates great mental discipline.