This refers to waking consciousness, and all life that is not spent asleep. The term “waking life” is used instead of “real life” because dreams are a real part of life: not just because they are experienced as real at the time, but also because they have real effects on waking life. We experience our dreams in both our brains and our bodies, and what happens in our dreams affects us in subsequent waking life, even if we don’t remember them. (If you have ever been angry at your lover for something they did in a dream, you will be well aware of the real effects dreams can have…)