now, you seem to be newer than I am at this stuff, but here we go.
an amplifier dies just that, amplifies. you buy them for applications where the signal from a source is not sufficient to drive a speaker.
now, if you want subs, then you will need an amplifier. most head units, or radios, cannot drive more than four door speakers alone, but usually have an rca output on the back if it's an aftermarket unit.
the amplifier you are looking at is a two channel amplifier that putsout roughly 60 watts by 2 channels at 4 ohms, meaning that 2 subs with a four ohm impedance can be wired one power channel and will receive sixty watts of power each.
to answer the next part of your post, you could run door speakers off of that amplifier, but not at the same time as the subwoofers.
if you plan to run subs from an amp like that, you'll need to turn on the amplifier low pass filter to remove any higher frequencies that the subs cannot reproduce effectively.
next, the number of channels are simply the number of speakers the unit can drive if you hook up one per channel.
most subwoofer amps are mono, or one. but it's okay to use a multi channel amplifier to run subwoofers, as long as you can filter out the lower frequencies.
the next consideration is power, make sure you can run at least 4 gauge wire from the battery to the amp, and make sure you use fuses, unless you like having 1300 degree wire burning your car if something goes wrong.
hopefully that's a spring board for you to learn from, and best of luck.
