Paul, there are two stages of amplification that take place, regardless of whether a receiver or a separate pre-amplifier plus amplifier are being used. The pre-amplifier first increases the voltage coming in from the player or other source component about 4-5 times; the amplifier then increases this voltage about 25-30 times more, so the net result is an increase of about 100-150 times, which is enough voltage to drive speakers to very loud levels.
The pre-amplifier section of the receiver or separate unit also controls the various functions which other replies have listed. The volume, for example, is controlled by a variable resistor which varies the amount of the incoming voltage which is subject to the fixed 100 or so times "gain" mentioned above from almost 100% to almost none.
A separate amplifier can't improve the sound unless what you have is inadequate for the volume levels needed. Your 3311 is rated at 125 watts per channel, and this is the one area of audio that can be relied on as accurate, since it's subject to legal regulations of the FTC. Your 3311 can drive your speakers to beyond safe(to your hearing)listening levels, and more isn't needed. As Kruncher quoted me above, unused headroom is simply that: unused.
Your equipment, with one exception, is excellent, and it's agreed that a quality sub is what will improve your listening experience.
Enjoy the music, not the equipment.