jfoutz has a pretty good answer, but as a former astronomer who studied triple systems I thought I would expand a little bit. The main reason this is important

jfoutz has a pretty good answer, but as a former astronomer who studied triple systems I thought I would expand a little bit. The main reason this is important is that it is data in favor of the hypothesis that Proxima Centauri is gravitationally bound to the rest of the Alpha Centauri system. If the Alpha Centauri system is triple system rather than a binary with another stars that just happens to be passing by, this could change our understanding of how this system formed. As it turns out, the dynamics of triple systems can in some cases be extremely interesting due to a phenomenon called Kozai-Lidov oscillations [1]. The idea here is that if the orbital plane of a tertiary companion is at high inclination relative to the inner binary, it can drive the orbit of the inner binary to high eccentricities over a long period of time. In this case, it is known that Proxima Centauri hosts a planet in its habitable zone. But the orbital dynamics of this planet may have been affected by the Alpha Centauri A/B binary. If the planet formed further away from Proxima, it may have migrated due to Kozai-Lidov oscillations. Furthermore, if Proxima is bound, its dynamical influence on the Alpha Cen A/B system may have prevented the formation of circumbinary planets, or disrupted the orbits of these planets. Indeed, one speculative idea is that Proxima's planet may have formed around Alpha Cen A/B, and then been kicked out and captured by Proxima Cen. [1]: https://en.wikipedia.org/wiki/Kozai_mechanism https://en.wikipedia.org/wiki/Kozai_mechanism