I kinda skimmed it. So from what I understand, they put a cooling layer behind regular solar panels. Panels get less efficient when they heat up so keeping them cool is where the extra efficiency comes from. The cooling layer is inspired by how plants cool themselves, it seems sort of similar to sweating in a way. Water moves through by capillary action, absorbs heat from the panel, and evaporates. Additionally they discuss:

• using salt water as input water, which will result in some clean water output. It seems you need to kinda flush the cooling layer at night to get rid of salt crystal build up, but this could be a nice bonus in less developed areas.
• use a condenser down the line to recover heat energy from the evaporated output water. Has the potential to raise total efficiency by a bunch of you can use the warm water for heating and the PV generated electricity for power.

They claim the cooling layer doesn't add much extra cost (6 months extra operation to recoup your investment). I wonder what the lifetime of the cooling layer is compared to the photovoltaics themselves. They use some natural fiber I think so maintenance could be an issue.