Current is measured in amps, not volts. The best way to describe the relationship between volts, amps, and ohms is to imagine a water main.
Voltage is the pressure of the water. Amps are the flow rate. Ohms are the size (diameter) of the pipe.
Battery capacity is measured in mAh, or milliamp-hours. A 2600 mAh battery like in the MVP 2.0 can push a 1 amp current for 2.6 hours. (2600 mA / 1000 mA = 2.6).
However, you can not determine the actual battery capacity left. What devices like the MVP 2.0 do is check the voltage. A battery's voltage drops as it is discharged -- it will start at 4.2 volts when fully charged, and will gradually drop as it is used. You can estimate the remaining battery capacity from this. Your cell phone does the exact same thing to show the battery meter. It measures the voltage, and estimates that the battery is 75% full, 50% full, etc.
VV/VW devices like the MVP 2.0 use electronic circuitry to boost or buck (reduce) the voltage from the battery. Think of it like a very small circuit-based transformer. If the battery voltage is 3.9 volts, and you set your MVP to 4.5 volts, it will boost the 3.9 volts to 4.5 volts, and if you set it to 3.6 volts, it will buck the 3.9 volts down to 3.6 volts.