Photosynthesis powers our biosphere and without it we'd be rather short of breath, but oxygenic photosynthesis is a tiny subset of what life has tried. In bacteria there are many different photoreactive molecules and several different photosynthetic processes - some use water as the reductant (hydrogen source), some use hydrogen neat, and some use hydrogen sulphide. Also the photosynthesis we know and love in familiar plants is quite fond of two rather narrow frequencies of visible light, but it's possible for biomolecules to grab several photons of light to get their power-boost from near-infrared (NIR) in the 1000 to 1400 nanometre wavelength range.

So what does this imply? According to these two studies...

Spectral signatures of photosynthesis I: Review of Earth organisms

...and its follow-up...

Spectral signatures of photosynthesis II: coevolution with other stars and the atmosphere on extrasolar worlds

...it means that M-dwarf stars can sustain oxygenic photosynthesis and might even allow land-based life, if their flares are of the milder variety. Most M-dwarfs flare - rapidly increase in x-ray and UV brightness for brief periods - but some flares are milder than others. A proper atmosphere is quite able to absorb harmful x-rays, but a bit of UV gets through, enough to inhibit life - but even the largest flares will only penetrate about 9 metres into water with their UV, so oceanic life is quite safe.

An who's to say that life can't adapt to UV and even find it useful? Perhaps by incorporating more metals into their metabolism organisms might usefully trap UV energy for biological processes?

In more immediate terms what it means is that we can fairly confidently hope to find habitable planets around even the smaller variety of stars - and since M-dwarfs make up 75% of stars in our immediate neighbourhood that's a good thing.