The biggest benefit to a solar cover is reducing evaporation at night. When the pool evaporates it looses a lot of heat (heat of evaporation) so there is a big benefit to using a solar cover at night.
During the day a solar cover can help reduce evaporative cooling, but it also reduces the amount of heat the bulk water is able to absorb from the sun.
The clearer the cover, the better heating of bulk pool water by the sun. A solar cover used during the sunlight hours can reduce the amount of chlorine consumption due to blocking some of the sun's UV light. The flip-side to this is that same UV blocking also reduces the oxidation that could be accomplished by the sun, so more chlorine is used/needed to do the oxidation.
Bottom line...during the day to gain heat: when the sun is on the pool, the wind is low, and the ambient air temperature is close to/above the pool temp, I leave the solar cover off. At night I would always keep the solar cover on unless your pool is too hot, or you are doing the shocking process.