Very few headunits have the ability to power a subwoofer, and those that do will only do it for subs with low power handling. Yes you could use a 2 channel amplifier, you'd bridge the 2 channels into a single channel. The best thing to use is a monoblock (single channel, designed for subs).
An amplifier does as the name suggests, amplifies the signal. Your headunit doesn't provide enough power for higher output equipment. When you install an amp you have another run of power cable coming from the battery (hence your power source) while the speaker/subwoofer signals are still coming from the headunit. So yeah, purpose - provide the power you need and produce a clearer signal than your headunit could make (unless you get a really sh*tty amp). Think about the size of an amplifier compared to a headunit. A headunit has it's own small internal amplifier (most cases) + all it's other circuitry all in that tiny little box compared to an amplifier which is alot larger and designated solely to amplifying the signal. Hope this helps, cheers, Bryce.