Coarse control generally sets the current/voltage in larger increments, i.e. 0.1V at a time. Fine control will set it in smaller increments, i.e. 0.001V at a time.
A simple google search would have answered that question for you.
Also, if you are going to hook up diodes directly to an adjustable power supply make sure it's a decent quality supply. Some supplies will throw out large voltage spikes that'll instantly kill your diode. I had to add a bunch of capacitors on the output of my last one to level out the voltage spike. That also means you need to short the outputs to discharge said capacitors (should do that anyway) before hooking up the diode, for similar reasons.
Like the names imply, the fine and coarse controls will work together to adjust the outputs that you want. For instance, if you wanted to set a voltage output to five volts, you would first put the fine control to its center position and then use the coarse control to get as close to the five volt setting that you want.
You might find that a tiny clockwise turn of the coarse control would shoot a little past a precise five volts and then a tiny counterclockwise turn of the coarse control would drop the voltage to slightly less than five volts.
No problem. When you have the coarse setting close to the voltage you want then you use the fine control where a large turn will make tiny changes in the voltage until you hit the exact setting you want. Adjust coarse first for large changes and then use fine to get the precise setting you want.