Explain in your own words how current and voltage are used in the welding process?

You mean electric welding. A current is a charged particle moving. That allows engineers to calculate the amount of metal deposited as a function of current. When that is done by an arc process, voltage might vary wildly. When no current is flowing, the voltage should not go high enough to make a large arc or to cause fatal injuries to people who touch the bare electrodes. (Injuries, perhaps, but not fatal.) You, as a welder, just do what the engineers tell you.