Solar cell efficiency refers to the portion of energy in the form of sunlight that can be converted via photovoltaics into electricity. The efficiency of the solar cells used in a photovoltaic system, in combination with latitude and climate, determines the annual energy output of the system.
The operating temperature plays a key role in the photovoltaic conversion process. Both the electrical efficiency and the power output of a photovoltaic module depend linearly on the operating temperature.
Efficiency of solar cell mainly depends on its band gap of materials, intensity of light, contact area, defect density along material interface, carrier lifetime of the materials, area of solar cell etc.
The efficiency and the photocurrent and voltage that you can extract from the solar cell are different things indeed. Efficiency is the measure of how many photons are converted into recoverable electrons by the combined effect of the cell voltage and the photocurrent and the resistances etc measured into the fill factor. The efficiency measure should not change that much with irradiance (irradiance meaning the amount of photons you send), except in the case of heating the cell too much. However, the photocurrent will change as much as less or more photons strike the cell and the voltage will change if the cell is heated for example.
There are lots of web tutorials that explain in detail what the I-V curve of a solar cell measures and how a solar cell works as well as the individual factors that influence FF, Voc, Isc and the whole efficiency.