Solder mask is a coating that is applied to a PCB to prevent solder from sticking to it.
It is not really necessary for hand-soldered boards, but is essential for boards that are soldered automatically using solder bath or reflow techniques.
There will usually be top and bottom solder masks, with separate Gerber files for each.
For saving the PCB production setup fee and fabrication fee and shipping fee, Green Solder mask is the most economic selection, and the others will cost little more.
