An amp is required as a head unit puts out around 50W and this amount of power will not be high enough to produce sound out of your sub. (Any noticeable sound anyway)
An amp (amplifier) amplifies the power output, which will give you a louder sound. Also amps tend to have less distortion then a standard head unit, so running all your speakers off an amp will give a better sound in most cases.
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.