The phrase "to influence the clouds" means having the power to control or change the outcome of a situation. It implies the ability to affect things beyond your immediate control. Full definition
To really appreciate the true solar effect on climate it is necessary to include chemical changes and total solar influenced cloud cover to see the real picture. (landscheidt.info)
Of course this is the response, if nothing else is influencing cloud properties / cover, but important enough for further investigation. (realclimate.org)
They regulate the amount of sunlight received by the surface and so influence evaporation from the surface, which in turn influences cloud formation. (eso.org)