Flow can be described as a lot of things. In martial arts it is often thought of being a point of clarity or auto pilot, sometimes referred to as "The Zone." In Japanese it is called Mushin or the point of "No Mind. " It's the point that a martial artist can reach where movements and reactions become automatic.
Unless you have experienced it yourself (several times) it's a little hard to truly describe, but visually and in a combative sense, the best examples I can give are Anderson Silva vs Yushin Okami and Forrest Griffin. There is a point in both of these fights where Anderson, "Enters the Matrix" as Joe Rogan put it, where he is on full overdrive. He sees punches, kicks and movements way before Yushin or Forrest know they are throwing them. He moves out of the way, ducks, dodges, feints past every kick and punch to deliver a brutal counter punch as they step into the pocket in frustration. He knocks both men off their feet with something that looks like a phantom punch. This effortless movement and cohesion of both mental and physical attributes is one of the highest levels an athlete or martial artist can reach.
There are several ways of achieving such high level reactions, first is thousands of hours learning a skill, secondly mental training, preparation, and meditation and lastly permanently storing countless sequences of body movement into your brain.
One way to fast track all of the above is to work with a slightly different kind of flow. In this case we mean a series of movements or techniques (often counter for counter) linked together into a set pattern or sequence. Working a flow drill this way is one of the best tactics you can apply in your daily training. High reps are great, but flow drills build a smooth consistency that directly transfers over to live sparing or competition. Flow drills also build your timing, sensitivity and awareness of potential submissions and positions. I personally cannot say enough about flow drills, they have gotten me very far in times when I had no instructor or limited training partners. The hardest part of working flow drills such as these is finding the right partner. You need a partner that will give you proper resistance and intensity while pushing you beyond what you're already accustomed too.
Check out this beautiful European Luta Livre Flow that details both offensive and defensive strategies.