The SVD of a protein conformation matrix is similar to a quasi-normal mode analysis in that it gives a set of vectors, called the left singular vector, which describe which direction each atom prefers to move in. The SVD also gives temporal information through the right singular vectors. These vectors can be thought of as the projection of the protein conformations onto a lower dimensional basis defined by the left singular vectors.
The elements of the right singular vector can be thought of as scaling the size of the left singular vector to describe where the atom is at each time-point or in each conformation. The right singular vectors are what are used to classify each structure for identifying conformational substates.