The Sanskrit word vinyasa can be translated as a continuous flow of poses coordinated with the breath.
Example, from a standing position with arms at side, you inhale as you raise arms straight overhead;
As you exhale, you bend forward at the waist as far as possible, knees straight;
On inhale, you raise torso about half way up;
On exhale, you jump both feet together backwards into Downward Dog position; etc, etc.
You continue moving from one pose to the next in conjunction with your inhalation/exhalation.
Power yoga is a style utilizing vinyasa technique.
Sun Salutations (Surya Namaskar) are another well known series of vinyasa.
"Power yoga" is a somewhat generic term for a Westernized style of Astanga Vinyasa (a style usually associated with Indian teacher Sri K. Pattahbi Jois).
Although most styles of Hatha yoga practice mindfulness of the breath while practicing any pose, in non-vinyasa styles (Iyengar, Anusara, Ananda, etc), you may hold a given pose for several breaths (or even several minutes), and without the focus on changing to next pose in time with breath.