There are many reasons why low energy neutrinos are interesting. If we can reliably measure their speed and energy, we can directly measure neutrino mass via Lorentz transform effects. Low energy neutrinos should also behave more like the hypothesized KeV mass dark matter of "warm dark matter" theories, which fit empirically measured dark matter effect better than "cold dark matter" which assumes heavier (MeV or more) and slower dark matter particles. High energy neutrinos, in contrast, move too fast to reproduce existing galactic structure and hence, less like warm dark matter.
At the very least, the Borexino experiment refines our understanding of the solar neutrino background, including its annual seasonal variations in cosmic muon detection which is explained almost entirely by seasonal variation in daily atmospheric temperatures (neutrino fluxes don't vary appreciably between day and night). These effects must be filtered out of any effort to detect other kinds of dark matter.
According to one of the authors of a recent study on the subject quoted at Science Daily (linked above):
Borexino is the only detector capable of observing the entire spectrum of solar neutrinos at once. Our results, the culmination of 20 years of research, greatly narrow the observation precision. The data confirm the neutrino oscillations, flavor changes and flow predicted by models of the sun and particle physics. . . . Our detector provides stringent tests of the three-neutrino oscillations model.
While the researcher quoted above appeared to confirm an "at least three" neutrino model, he was coy on the extent to which the data might support a model with four or more neutrinos, as other experiments in the last year, have indicated.
A September 30, 2011 publication from the experiment concluded that:
The rate of neutrino-electron elastic scattering interactions from 862 keV 7Be solar neutrinos in Borexino is determined to be 46.0±1.5(stat)-1.6+1.5(syst) counts/(day·100 ton). This corresponds to a νe-equivalent 7Be solar neutrino flux of (3.10±0.15)×10^9 cm-2 s-1 and, under the assumption of νe transition to other active neutrino flavours, yields an electron neutrino survival probability of 0.51±0.07 at 862 keV.
The no flavor change hypothesis is ruled out at 5.0 σ.
A global solar neutrino analysis with free fluxes determines Φpp=6.06-0.06+0.02×10^10 cm-2 s-1 and ΦCNO < 1.3×10^9 cm-2 s-1 (95% C.L.). These results significantly improve the precision with which the Mikheyev-Smirnov-Wolfenstein large mixing angle neutrino oscillation model is experimentally tested at low energy.
As background regarding the MSW model:
[A]mong the different possible solutions of the solar neutrino problem, the Mikheyev–Smirnov–Wolfenstein (MSW) large mixing angle (LMA) solution is the presently preferred one, draws a picture of the involved flavor symmetries and their breaking mechanisms that differs remarkably from the early approaches, which have been applied to the quark sector. In the “standard” parameterization, the MSW LMA solution implies that we have a bilarge mixing scenario in the lepton sector in which the solar mixing angle θ12 is large, but not necessarily close to maximal, the atmospheric mixing angle θ23 is nearly maximal, and the reactor mixing angle θ13 is small. Clearly, this is in sharp contrast to the quark sector in which all mixing angles are small and it indicates that the flavor symmetries act on the third generation too.
Borexino also turns out to place rather weak limitations of the value of the mixing angle theta 13. Other experiments have pointed to a low but non-zero value for this mixing angle. For example, the SNO experiment estimated it to be 4.2 degrees to 9.4 degrees. But, Borexino can't rule out a zero value and the maximum value its data are consistent with is slightly greatly than the maximum value set by the T2K experiment, for example. Recent values of all of the oscillation parameters (the three mixing angles and the two neutrino mass differences) can be found here.
Basically, Borexino doesn't add much precision to existing measurements, but does make those measurements more robust by reaching consistent results with an independent data set produced using a different kind of experimental setup.
The Borexino experiment provides better bounds on the mass differences between neutrino mass eigenvalues and places strict limits on differences on any differences in oscillation rates between neutrinos and antineutrinos. The LMA model favored by the data due to the low level of day-night asymmetry observed at Borexino implies that the square of the difference in mass between the first and second neutrino mass eigenvalues is on the order of 10^-5 eV^2, while the empirically difavored LOW model against which was compared suggests that the value is 10^-7 eV^2:
[T]he reported value of [day-night asymmetry in solar neutrino flux] A =0.001 +/- 0.012 (stat) +/- 0.007 (syst) completely rules out the LOW region of the neutrino parameter space using only the solar neutrino data without any direct reference to the reactor antineutrinos. This experimentally establishes that the neutrino and antineutrino mixings are indeed identical.
Of course, either way, neutrino masses are still tiny.