Voltage and Amperes are two sides of the same coin. One way to picture it is a comparison to water flow through a pipe.
Volts are to electricity as pressure is to water. How hard are the electrons being pushed through the circuit. In a car, at 12-14V, in your house, 120V... or 240 depending where you are. At the power transformer outside your house? A LOT more. Indeed the transformer is there to siphon off a bit of the high voltage wire's pressure, and then wind it through thin, thick sheets of metal, effectively reducing the pressure (voltage) so that all of your electronics don't fry.
Amperes are to electricity as flow rate is to water. How much energy (power?) is being delivered at the above (volts) pressure. Wattage is not something that you really should ever pay attention to - its not a good measure of actual power requirements due to difference in the efficiency producing said wattage. Amperes is.
Your alternator, assuming its stock, produces at its peak 70-100amps, depending on what car you drive. Generally the stock ones are designed to product above 10 amps above top current draw of all the car electronics enabled at once. Not a lot of headroom for car audio. But if you don't usually blast your system, and you're looking at max draw of say 50 amps or so (where my last system was at, 450W RMS), its actual draw will be much lower. Your battery is able to absorb the shocks when the bass hits so that your alternator doesn't actually need to be able to exceed that maximum at all times.
Last thing to touch on is the max ampacity of your power wires. Just google a chart, but basically, the bigger the gauge, the bigger the cross-sectional area, the more amps the wire can carry without overheating and starting a fire. This and other factors allow wider power wires to carry the additional current when the subwoofer hits. Hence, a Big 3 upgrade helps your car's circuit system to absorb those bass his shocks.