Vinyasa, as I have been taught, means to place together in an intentional way, to create consciousness in motion. In the Ashtanga Vinyasa yoga tradition, every breath is counted and corresponds to a specific movement in and out of every pose, or asana. Vinyasa yoga practice can be compared to a physical japa practice, with the asanas acting like the beads on a mala, and every breath creating the string upon which the beads are strung together. Just as with a mala, you can use your vinyasa practice as a kind of physical adornment or you can use it as a spiritual practice to transform your whole life. It is a meditation in movement of the body-mind that rides on the breath.
Many of the various approaches to “Power Yoga” & “Flow Yoga” (heated and non-heated) that can be found in yoga studios and health clubs today can be considered derivatives of “Vinyasa” and are often, according to the teacher’s teacher’s yoga training, a kind of adaptation or variation of the Ashtanga Vinyasa practice.