I'll take a shot at this. Essentially they're saying that they've found evidence that alternative theories about gravitation (non-Einsteinian theories) that ar

I'll take a shot at this. Essentially they're saying that they've found evidence that alternative theories about gravitation (non-Einsteinian theories) that are strictly simpler (like classical Newtonian gravity) are not consistent with the observations. Here scalar means that the field that describes the phenomenon can be described as a single scalar value at each point of space, like density, as is the case of sound waves. Vector is more complex; although "charge" is a scalar, electromagnetic waves do not propagate by inducing charge in the surrounding space, but by propagating through the free-space Maxwell equation (that is, where the charge density is zero). So the polarization of an electromagnetic wave can be described by a single vector at a point, and the measurement of the magnitude of the wave will depend on how closely the measurement axis corresponds to the polarization axis for a polarized wave. For a general wave, it can be described as some linear combination of the orthogonal polarizations. Although "tensor" is a general linear object of which vectors are a subset, in this case of gravitational waves, we require a 2-tensor to describe the polarization of the wave. Effectively that means the polarization (the strength of the signal with respect to a given detector) can only be described by two independent vector that describe the evolution of the wave. Since the three detectors (Ligo Hanford, Ligo Livingston, and Virgo) are not exactly aligned with one another, it should be possible to get good evidence that the polarization cannot be adequately described by the superposition of two orthogonal vectors, but instead two independent pairs of orthogonal vectors.