To start off, high-end car audio systems are comprised of three main things: Speakers, Headunit, and Ampilifier. The sound starts in the head-unit as a cd or ipod connection. From there it travels to the amplifier. The amplifier takes that "small" signal and makes it REALLY BIG! Think of it like a popcorn kernel. The un-popped kernel comes from the headunit and the amplifier blows it up and makes it bigger. Then, the signal travels from the amplifier to the speakers which make all of the glorious sound waves we hear! To answer the rest of your question: Subwoofers are used to produce sound waves with a frequency of about 80hz or lower. They fill out the low-end of your music and can add Boom-Boom if you would like.
Peak wattage refers to the amount of power (supplied by the amplifier) that the speaker can take before ruining the internal components. It is best to stay just below that number.
1, 2, and 3 channel amps vary based on the number of outputs they have. A one channel, or mono amp is used to power a single output, usually a subwoofer. A 2 channel amp has two outputs, usually left and right, that is used to power either two subwoofers of a Left and Right speaker set. There are amps that go all the way up to 5 channels to power 4 sets of speakers and a sub.
You do not NEED a sub in your car, but they will make your system sound better. Subwoofers fill our your music and add the low-end that you would typically miss with just stock speakers.
Take at look at the manufacturers web-site to find the specs on your headunit. Then take a look at your speakers spec sheet to see what the RMS and max wattages are. Most of the time, after-market speakers will require an amplifier, plus, using an aftermarket (not in Headunit) amplifier will make your system sound better.
The difference between two and three way speakers is the physical number of drivers combined into one unit. A two way speaker has a main woofer cone and a tweeter in one unit. A three-way speaker has a woofer cone, a mid-range driver, and a tweeter all in one enclosure.