Do data points mean Eigenfaces in higher dimensional space?
Each blue data point in the animated picture stands for an image of a face whose dimension is much higher in the context of Eigenfaces for Recognition. They are the original data points. It does NOT mean Eigenfaces.

When the long swinging black solid rod becomes still under the "viscous friction" exerted by the red lines, its direction is the most significant eigenface in that context, which is defined as an eigenvector of the biggest eigenvalue of the covariance matrix of the face images. The projection of the blue points onto that long black rod viewed as vectors starting from the center of the blue points is the first principal component.