Flow is being completely involved in an activity for its own sake. The ego falls away. Time flies. Every action, movement, and thought follows inevitably from the previous one.
Mihaly Csikszentmihalyi
The term "flow state" was, to the best of my knowledge, coined and popularised by Mihaly Csikszentmihalyi (you better believe I didn't type that out, Ctrl V ftw). Flow describes a mental-physiological state whereby a person is completely absorbed in performing an action, and is at once perfectly consciously and unconsciously aware of what they are doing. That is not a contradiction. A rider of a bicycle or motorcycle at high speed consciously processes sensory data, the unconscious mind is passing data into consciousness, the body is acting under both conscious and unconscious control and acting/reacting extremely quickly. The same can be true during communication using language, performance of strenuous physical activity, or meditation.
Flow states are generally found when an individual has achieved some level of mastery of an activity. They are fully absorbed in the task, at once operating smoothly and confidently but also managing the challenge. The feeling of awareness-no awareness is almost impossible to describe, it is recognised by experience. It can be observed as a preponderance of theta-pattern brain activity as opposed to the much more common alpha and beta patterns. Flow states in elite athletes are heavily studied and documented, because that's where the money is.
I have a hypothesis that life in a modern developed society may tend to insulate people from experiencing flow, and that we may find a benefit in seeking out and achieving flow states. I wonder if jaguars experience flow. This was probably written in a flow state.